<?xml version="1.0" encoding="UTF-8"?>

<!--XBRL Document Created with the Workiva Platform-->
<!--Copyright 2024 Workiva-->
<!--r:642a305a-0bac-4e98-a71a-55634cb84541,g:ba5c40e7-9765-4ce9-97f9-3f97a7514c15-->
<link:linkbase xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xbrldt="http://xbrl.org/2005/xbrldt" xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd">
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/all" xlink:type="simple" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#all"/>
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:type="simple" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#hypercube-dimension"/>
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:type="simple" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#dimension-default"/>
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:type="simple" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#dimension-domain"/>
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/domain-member" xlink:type="simple" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#domain-member"/>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/UnauditedCondensedConsolidatedBalanceSheets" xlink:type="simple" xlink:href="hg-20240930.xsd#UnauditedCondensedConsolidatedBalanceSheets"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/UnauditedCondensedConsolidatedBalanceSheets" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems_128e9f2e-a270-4be6-928f-008210504c53" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable_5e719517-e710-430c-80e5-005b8d760749" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_StatementLineItems_128e9f2e-a270-4be6-928f-008210504c53" xlink:to="loc_us-gaap_StatementTable_5e719517-e710-430c-80e5-005b8d760749" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementClassOfStockAxis_3f7f262d-3440-483a-9d07-9238425b9dd7" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementClassOfStockAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_StatementTable_5e719517-e710-430c-80e5-005b8d760749" xlink:to="loc_us-gaap_StatementClassOfStockAxis_3f7f262d-3440-483a-9d07-9238425b9dd7" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain_3f7f262d-3440-483a-9d07-9238425b9dd7_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ClassOfStockDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_StatementClassOfStockAxis_3f7f262d-3440-483a-9d07-9238425b9dd7" xlink:to="loc_us-gaap_ClassOfStockDomain_3f7f262d-3440-483a-9d07-9238425b9dd7_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain_43c01fdd-8e30-4c13-af79-d86a5c805988" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ClassOfStockDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_StatementClassOfStockAxis_3f7f262d-3440-483a-9d07-9238425b9dd7" xlink:to="loc_us-gaap_ClassOfStockDomain_43c01fdd-8e30-4c13-af79-d86a5c805988" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassAMember_de5a1729-fcea-4459-adcf-dda3dc621552" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonClassAMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockDomain_43c01fdd-8e30-4c13-af79-d86a5c805988" xlink:to="loc_us-gaap_CommonClassAMember_de5a1729-fcea-4459-adcf-dda3dc621552" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassBMember_e2fb251f-1c8f-4b55-abba-43a26f5b172c" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonClassBMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockDomain_43c01fdd-8e30-4c13-af79-d86a5c805988" xlink:to="loc_us-gaap_CommonClassBMember_e2fb251f-1c8f-4b55-abba-43a26f5b172c" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassCMember_1852fa01-1643-4618-b727-bb9fb07ef115" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonClassCMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockDomain_43c01fdd-8e30-4c13-af79-d86a5c805988" xlink:to="loc_us-gaap_CommonClassCMember_1852fa01-1643-4618-b727-bb9fb07ef115" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis_dc92a780-6a64-4c83-9d1c-10faf8677f25" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinancialInstrumentAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_StatementTable_5e719517-e710-430c-80e5-005b8d760749" xlink:to="loc_us-gaap_FinancialInstrumentAxis_dc92a780-6a64-4c83-9d1c-10faf8677f25" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_dc92a780-6a64-4c83-9d1c-10faf8677f25_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_FinancialInstrumentAxis_dc92a780-6a64-4c83-9d1c-10faf8677f25" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_dc92a780-6a64-4c83-9d1c-10faf8677f25_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_5067bc86-3501-443d-a0ef-96ab10a1c910" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_FinancialInstrumentAxis_dc92a780-6a64-4c83-9d1c-10faf8677f25" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_5067bc86-3501-443d-a0ef-96ab10a1c910" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FixedMaturitiesMember_f0fde1b1-14d7-4d1d-9c55-3eabfd39fc0e" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FixedMaturitiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_5067bc86-3501-443d-a0ef-96ab10a1c910" xlink:to="loc_us-gaap_FixedMaturitiesMember_f0fde1b1-14d7-4d1d-9c55-3eabfd39fc0e" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortTermInvestmentsMember_c7066921-a90a-42b3-b2e3-900b3fbe54b9" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShortTermInvestmentsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_5067bc86-3501-443d-a0ef-96ab10a1c910" xlink:to="loc_us-gaap_ShortTermInvestmentsMember_c7066921-a90a-42b3-b2e3-900b3fbe54b9" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsAbstract_9463e5ba-e841-4820-9afe-c84565117845" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AssetsAbstract"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StatementLineItems_128e9f2e-a270-4be6-928f-008210504c53" xlink:to="loc_us-gaap_AssetsAbstract_9463e5ba-e841-4820-9afe-c84565117845" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradingSecuritiesDebt_dad42227-425c-498b-8f85-37cce5bbc2da" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TradingSecuritiesDebt"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AssetsAbstract_9463e5ba-e841-4820-9afe-c84565117845" xlink:to="loc_us-gaap_TradingSecuritiesDebt_dad42227-425c-498b-8f85-37cce5bbc2da" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AlternativeInvestment_290fba56-6002-4ae9-9fe4-c8da57ebc8fa" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AlternativeInvestment"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AssetsAbstract_9463e5ba-e841-4820-9afe-c84565117845" xlink:to="loc_us-gaap_AlternativeInvestment_290fba56-6002-4ae9-9fe4-c8da57ebc8fa" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Investments_30c78903-6801-4a5a-b082-e95f4aa3b8a2" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_Investments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AssetsAbstract_9463e5ba-e841-4820-9afe-c84565117845" xlink:to="loc_us-gaap_Investments_30c78903-6801-4a5a-b082-e95f4aa3b8a2" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue_42ea462e-f8d5-42b1-a416-f38c3338aa8d" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AssetsAbstract_9463e5ba-e841-4820-9afe-c84565117845" xlink:to="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue_42ea462e-f8d5-42b1-a416-f38c3338aa8d" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCashAndCashEquivalents_ee9f1eb5-348a-4cde-8e15-7b3d0d11bc48" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RestrictedCashAndCashEquivalents"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AssetsAbstract_9463e5ba-e841-4820-9afe-c84565117845" xlink:to="loc_us-gaap_RestrictedCashAndCashEquivalents_ee9f1eb5-348a-4cde-8e15-7b3d0d11bc48" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsReceivableAtCarryingValue_75118350-124b-40f8-8961-234b219a3656" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PremiumsReceivableAtCarryingValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AssetsAbstract_9463e5ba-e841-4820-9afe-c84565117845" xlink:to="loc_us-gaap_PremiumsReceivableAtCarryingValue_75118350-124b-40f8-8961-234b219a3656" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverablesOnPaidLosses_91a75839-9a6c-4377-9fcc-d58ccb944f77" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ReinsuranceRecoverablesOnPaidLosses"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AssetsAbstract_9463e5ba-e841-4820-9afe-c84565117845" xlink:to="loc_us-gaap_ReinsuranceRecoverablesOnPaidLosses_91a75839-9a6c-4377-9fcc-d58ccb944f77" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredPolicyAcquisitionCosts_bc883d3f-e074-4d33-af52-70fb214d48d3" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredPolicyAcquisitionCosts"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AssetsAbstract_9463e5ba-e841-4820-9afe-c84565117845" xlink:to="loc_us-gaap_DeferredPolicyAcquisitionCosts_bc883d3f-e074-4d33-af52-70fb214d48d3" xlink:type="arc" order="8"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments_9ccf1c40-f0cb-4681-9cdc-70c1f910c189" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AssetsAbstract_9463e5ba-e841-4820-9afe-c84565117845" xlink:to="loc_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments_9ccf1c40-f0cb-4681-9cdc-70c1f910c189" xlink:type="arc" order="9"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivablesFromBrokersDealersAndClearingOrganizations_9669063b-39f7-4a1a-af10-e396ae929844" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ReceivablesFromBrokersDealersAndClearingOrganizations"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AssetsAbstract_9463e5ba-e841-4820-9afe-c84565117845" xlink:to="loc_us-gaap_ReceivablesFromBrokersDealersAndClearingOrganizations_9669063b-39f7-4a1a-af10-e396ae929844" xlink:type="arc" order="10"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidReinsurancePremiums_7198d951-831f-4b30-b60d-98430812cc8d" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PrepaidReinsurancePremiums"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AssetsAbstract_9463e5ba-e841-4820-9afe-c84565117845" xlink:to="loc_us-gaap_PrepaidReinsurancePremiums_7198d951-831f-4b30-b60d-98430812cc8d" xlink:type="arc" order="11"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IntangibleAssetsNetExcludingGoodwill_34c13a79-0f3e-4ab8-aab9-cd885bd51395" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IntangibleAssetsNetExcludingGoodwill"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AssetsAbstract_9463e5ba-e841-4820-9afe-c84565117845" xlink:to="loc_us-gaap_IntangibleAssetsNetExcludingGoodwill_34c13a79-0f3e-4ab8-aab9-cd885bd51395" xlink:type="arc" order="12"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssets_404cb7b8-ffc7-46ba-b32b-bbcbf814770c" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherAssets"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AssetsAbstract_9463e5ba-e841-4820-9afe-c84565117845" xlink:to="loc_us-gaap_OtherAssets_404cb7b8-ffc7-46ba-b32b-bbcbf814770c" xlink:type="arc" order="13"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets_936bc6c7-837a-490d-8bf5-5e32d54f3ba4" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_Assets"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AssetsAbstract_9463e5ba-e841-4820-9afe-c84565117845" xlink:to="loc_us-gaap_Assets_936bc6c7-837a-490d-8bf5-5e32d54f3ba4" xlink:type="arc" order="14"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract_1f4b4d10-d082-4cf3-8838-2ce822d91da8" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LiabilitiesAndStockholdersEquityAbstract"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StatementLineItems_128e9f2e-a270-4be6-928f-008210504c53" xlink:to="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract_1f4b4d10-d082-4cf3-8838-2ce822d91da8" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAbstract_1daaa7e4-1ba4-4e9e-a709-751dbe3685db" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LiabilitiesAbstract"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract_1f4b4d10-d082-4cf3-8838-2ce822d91da8" xlink:to="loc_us-gaap_LiabilitiesAbstract_1daaa7e4-1ba4-4e9e-a709-751dbe3685db" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense_477a6f1a-b131-4ec2-900f-3507b80f94c2" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilitiesAbstract_1daaa7e4-1ba4-4e9e-a709-751dbe3685db" xlink:to="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense_477a6f1a-b131-4ec2-900f-3507b80f94c2" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnearnedPremiums_a2fd3590-e7b5-47d4-87a9-734be44580e5" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_UnearnedPremiums"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilitiesAbstract_1daaa7e4-1ba4-4e9e-a709-751dbe3685db" xlink:to="loc_us-gaap_UnearnedPremiums_a2fd3590-e7b5-47d4-87a9-734be44580e5" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsurancePayable_3c093cd6-ff8c-4181-8e14-db77c031032b" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ReinsurancePayable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilitiesAbstract_1daaa7e4-1ba4-4e9e-a709-751dbe3685db" xlink:to="loc_us-gaap_ReinsurancePayable_3c093cd6-ff8c-4181-8e14-db77c031032b" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_PayablesToBrokerDealersAndClearingOrganizations_b6dfeaa7-b590-47a6-9030-f4f69d489ed2" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_PayablesToBrokerDealersAndClearingOrganizations"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilitiesAbstract_1daaa7e4-1ba4-4e9e-a709-751dbe3685db" xlink:to="loc_srt_PayablesToBrokerDealersAndClearingOrganizations_b6dfeaa7-b590-47a6-9030-f4f69d489ed2" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebt_31220b6d-82d3-4091-a5dc-3150a9131b04" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LongTermDebt"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilitiesAbstract_1daaa7e4-1ba4-4e9e-a709-751dbe3685db" xlink:to="loc_us-gaap_LongTermDebt_31220b6d-82d3-4091-a5dc-3150a9131b04" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent_31e8733b-b25b-451d-b62b-fb52a4a126b6" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilitiesAbstract_1daaa7e4-1ba4-4e9e-a709-751dbe3685db" xlink:to="loc_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent_31e8733b-b25b-451d-b62b-fb52a4a126b6" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilities_d06ef210-af88-4181-b434-a2b16cf2dc9c" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherLiabilities"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilitiesAbstract_1daaa7e4-1ba4-4e9e-a709-751dbe3685db" xlink:to="loc_us-gaap_OtherLiabilities_d06ef210-af88-4181-b434-a2b16cf2dc9c" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities_46d26137-b644-4dff-ba78-ba05bca4f0a4" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_Liabilities"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilitiesAbstract_1daaa7e4-1ba4-4e9e-a709-751dbe3685db" xlink:to="loc_us-gaap_Liabilities_46d26137-b644-4dff-ba78-ba05bca4f0a4" xlink:type="arc" order="8"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_227f966d-03f2-41ff-abb6-0f202a941c2e" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract_1f4b4d10-d082-4cf3-8838-2ce822d91da8" xlink:to="loc_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_227f966d-03f2-41ff-abb6-0f202a941c2e" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityAbstract_28e71a78-52f4-41f0-af5d-5d1f94475322" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockholdersEquityAbstract"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract_1f4b4d10-d082-4cf3-8838-2ce822d91da8" xlink:to="loc_us-gaap_StockholdersEquityAbstract_28e71a78-52f4-41f0-af5d-5d1f94475322" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValue_4097c6af-5b53-4ef8-bd0f-faf03d725d8d" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StockholdersEquityAbstract_28e71a78-52f4-41f0-af5d-5d1f94475322" xlink:to="loc_us-gaap_CommonStockValue_4097c6af-5b53-4ef8-bd0f-faf03d725d8d" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapital_bf7ae58d-4f9e-4eca-924d-d045a9391b85" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AdditionalPaidInCapital"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StockholdersEquityAbstract_28e71a78-52f4-41f0-af5d-5d1f94475322" xlink:to="loc_us-gaap_AdditionalPaidInCapital_bf7ae58d-4f9e-4eca-924d-d045a9391b85" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_8c286556-92bd-4e61-9de6-8cb2d6a9bf83" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StockholdersEquityAbstract_28e71a78-52f4-41f0-af5d-5d1f94475322" xlink:to="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_8c286556-92bd-4e61-9de6-8cb2d6a9bf83" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsAccumulatedDeficit_840c567a-6e59-40a1-9e8b-a74db2c5293c" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RetainedEarningsAccumulatedDeficit"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StockholdersEquityAbstract_28e71a78-52f4-41f0-af5d-5d1f94475322" xlink:to="loc_us-gaap_RetainedEarningsAccumulatedDeficit_840c567a-6e59-40a1-9e8b-a74db2c5293c" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity_bf9b9497-8da3-4356-a43c-4af7296c31f7" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockholdersEquity"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StockholdersEquityAbstract_28e71a78-52f4-41f0-af5d-5d1f94475322" xlink:to="loc_us-gaap_StockholdersEquity_bf9b9497-8da3-4356-a43c-4af7296c31f7" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquity_8eb408cd-091a-4e05-ab68-cb89373adca4" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract_1f4b4d10-d082-4cf3-8838-2ce822d91da8" xlink:to="loc_us-gaap_LiabilitiesAndStockholdersEquity_8eb408cd-091a-4e05-ab68-cb89373adca4" xlink:type="arc" order="4"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/UnauditedCondensedConsolidatedBalanceSheetsParenthetical" xlink:type="simple" xlink:href="hg-20240930.xsd#UnauditedCondensedConsolidatedBalanceSheetsParenthetical"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/UnauditedCondensedConsolidatedBalanceSheetsParenthetical" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems_afea4e6d-3ca1-447d-a0a9-ea2682582f9c" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable_49784451-36e9-4de3-b0f1-8ca700f683f0" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_StatementLineItems_afea4e6d-3ca1-447d-a0a9-ea2682582f9c" xlink:to="loc_us-gaap_StatementTable_49784451-36e9-4de3-b0f1-8ca700f683f0" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementClassOfStockAxis_1b24e51d-0a96-4ea6-a454-f3a4c979fc3f" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementClassOfStockAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_StatementTable_49784451-36e9-4de3-b0f1-8ca700f683f0" xlink:to="loc_us-gaap_StatementClassOfStockAxis_1b24e51d-0a96-4ea6-a454-f3a4c979fc3f" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain_1b24e51d-0a96-4ea6-a454-f3a4c979fc3f_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ClassOfStockDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_StatementClassOfStockAxis_1b24e51d-0a96-4ea6-a454-f3a4c979fc3f" xlink:to="loc_us-gaap_ClassOfStockDomain_1b24e51d-0a96-4ea6-a454-f3a4c979fc3f_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain_ddeb1790-4fe1-406d-9ec5-b67e0564db9a" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ClassOfStockDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_StatementClassOfStockAxis_1b24e51d-0a96-4ea6-a454-f3a4c979fc3f" xlink:to="loc_us-gaap_ClassOfStockDomain_ddeb1790-4fe1-406d-9ec5-b67e0564db9a" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassAMember_becccb9c-5dcb-4247-8cd0-7b8703f65dd6" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonClassAMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockDomain_ddeb1790-4fe1-406d-9ec5-b67e0564db9a" xlink:to="loc_us-gaap_CommonClassAMember_becccb9c-5dcb-4247-8cd0-7b8703f65dd6" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassBMember_4307157e-b39c-49df-bbad-f553dbd7c487" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonClassBMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockDomain_ddeb1790-4fe1-406d-9ec5-b67e0564db9a" xlink:to="loc_us-gaap_CommonClassBMember_4307157e-b39c-49df-bbad-f553dbd7c487" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassCMember_70d98d40-9329-4849-b3c7-2644aa995c41" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonClassCMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockDomain_ddeb1790-4fe1-406d-9ec5-b67e0564db9a" xlink:to="loc_us-gaap_CommonClassCMember_70d98d40-9329-4849-b3c7-2644aa995c41" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis_62d7e359-b911-49b2-a691-81cc64aabd68" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinancialInstrumentAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_StatementTable_49784451-36e9-4de3-b0f1-8ca700f683f0" xlink:to="loc_us-gaap_FinancialInstrumentAxis_62d7e359-b911-49b2-a691-81cc64aabd68" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_62d7e359-b911-49b2-a691-81cc64aabd68_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_FinancialInstrumentAxis_62d7e359-b911-49b2-a691-81cc64aabd68" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_62d7e359-b911-49b2-a691-81cc64aabd68_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_513190b7-dc86-4270-a71d-0bae87935a88" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_FinancialInstrumentAxis_62d7e359-b911-49b2-a691-81cc64aabd68" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_513190b7-dc86-4270-a71d-0bae87935a88" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FixedMaturitiesMember_38864fd4-ca87-4165-8ab8-87848bacc410" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FixedMaturitiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_513190b7-dc86-4270-a71d-0bae87935a88" xlink:to="loc_us-gaap_FixedMaturitiesMember_38864fd4-ca87-4165-8ab8-87848bacc410" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortTermInvestmentsMember_8095dbc0-6462-445a-a0cc-5fa1e355ffce" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShortTermInvestmentsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_513190b7-dc86-4270-a71d-0bae87935a88" xlink:to="loc_us-gaap_ShortTermInvestmentsMember_8095dbc0-6462-445a-a0cc-5fa1e355ffce" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradingSecuritiesDebtAmortizedCost_66f1f54b-7bc7-4c4d-a1d4-2444345e8d94" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TradingSecuritiesDebtAmortizedCost"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StatementLineItems_afea4e6d-3ca1-447d-a0a9-ea2682582f9c" xlink:to="loc_us-gaap_TradingSecuritiesDebtAmortizedCost_66f1f54b-7bc7-4c4d-a1d4-2444345e8d94" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentOwnedAtCost_b8c5534c-c69d-45ae-beed-3741765f95af" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InvestmentOwnedAtCost"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StatementLineItems_afea4e6d-3ca1-447d-a0a9-ea2682582f9c" xlink:to="loc_us-gaap_InvestmentOwnedAtCost_b8c5534c-c69d-45ae-beed-3741765f95af" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorized_fa9eeca3-4078-4a8c-8331-7b781635f56b" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockSharesAuthorized"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StatementLineItems_afea4e6d-3ca1-447d-a0a9-ea2682582f9c" xlink:to="loc_us-gaap_CommonStockSharesAuthorized_fa9eeca3-4078-4a8c-8331-7b781635f56b" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockParOrStatedValuePerShare_b1b4d891-d8d3-4450-8aeb-e57ddd18bd5c" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockParOrStatedValuePerShare"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StatementLineItems_afea4e6d-3ca1-447d-a0a9-ea2682582f9c" xlink:to="loc_us-gaap_CommonStockParOrStatedValuePerShare_b1b4d891-d8d3-4450-8aeb-e57ddd18bd5c" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesIssued_30b26dc2-dc0a-4451-8351-2f606fee2f9e" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockSharesIssued"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StatementLineItems_afea4e6d-3ca1-447d-a0a9-ea2682582f9c" xlink:to="loc_us-gaap_CommonStockSharesIssued_30b26dc2-dc0a-4451-8351-2f606fee2f9e" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding_c097b816-fc88-4e65-a151-f82922daa863" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockSharesOutstanding"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StatementLineItems_afea4e6d-3ca1-447d-a0a9-ea2682582f9c" xlink:to="loc_us-gaap_CommonStockSharesOutstanding_c097b816-fc88-4e65-a151-f82922daa863" xlink:type="arc" order="5"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/UnauditedCondensedConsolidatedStatementsofShareholdersEquity" xlink:type="simple" xlink:href="hg-20240930.xsd#UnauditedCondensedConsolidatedStatementsofShareholdersEquity"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/UnauditedCondensedConsolidatedStatementsofShareholdersEquity" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems_c3f9d076-9eed-4198-9af0-a2da28f63706" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable_ec36a884-28b7-4a51-be49-9e1401fdadde" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_StatementLineItems_c3f9d076-9eed-4198-9af0-a2da28f63706" xlink:to="loc_us-gaap_StatementTable_ec36a884-28b7-4a51-be49-9e1401fdadde" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis_36564b1a-c4dc-499e-9aca-dc1e928568ed" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_StatementTable_ec36a884-28b7-4a51-be49-9e1401fdadde" xlink:to="loc_us-gaap_StatementEquityComponentsAxis_36564b1a-c4dc-499e-9aca-dc1e928568ed" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain_36564b1a-c4dc-499e-9aca-dc1e928568ed_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EquityComponentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_StatementEquityComponentsAxis_36564b1a-c4dc-499e-9aca-dc1e928568ed" xlink:to="loc_us-gaap_EquityComponentDomain_36564b1a-c4dc-499e-9aca-dc1e928568ed_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain_5319792b-d979-43f8-bb8a-bb8f63f63d77" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EquityComponentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_StatementEquityComponentsAxis_36564b1a-c4dc-499e-9aca-dc1e928568ed" xlink:to="loc_us-gaap_EquityComponentDomain_5319792b-d979-43f8-bb8a-bb8f63f63d77" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember_5960fe46-5020-4f9c-9a47-30aa7b24c2b3" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_EquityComponentDomain_5319792b-d979-43f8-bb8a-bb8f63f63d77" xlink:to="loc_us-gaap_CommonStockMember_5960fe46-5020-4f9c-9a47-30aa7b24c2b3" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapitalMember_f1abc200-575d-4dcf-a0b2-8c4f7230af62" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AdditionalPaidInCapitalMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_EquityComponentDomain_5319792b-d979-43f8-bb8a-bb8f63f63d77" xlink:to="loc_us-gaap_AdditionalPaidInCapitalMember_f1abc200-575d-4dcf-a0b2-8c4f7230af62" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember_0a2c471c-ff50-4f35-8ba2-e8cf9b87e686" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_EquityComponentDomain_5319792b-d979-43f8-bb8a-bb8f63f63d77" xlink:to="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember_0a2c471c-ff50-4f35-8ba2-e8cf9b87e686" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsMember_f36cfa1e-d5b4-4941-af9e-58d1a04755c0" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RetainedEarningsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_EquityComponentDomain_5319792b-d979-43f8-bb8a-bb8f63f63d77" xlink:to="loc_us-gaap_RetainedEarningsMember_f36cfa1e-d5b4-4941-af9e-58d1a04755c0" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_e05918ad-55c0-4bd0-95c7-81cc801e07ed" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncreaseDecreaseInStockholdersEquityRollForward"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StatementLineItems_c3f9d076-9eed-4198-9af0-a2da28f63706" xlink:to="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_e05918ad-55c0-4bd0-95c7-81cc801e07ed" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity_f332276b-2932-42a3-8983-72171d9ac1c9" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockholdersEquity"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_e05918ad-55c0-4bd0-95c7-81cc801e07ed" xlink:to="loc_us-gaap_StockholdersEquity_f332276b-2932-42a3-8983-72171d9ac1c9" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueNewIssues_e75111ff-f402-4422-8097-da66d9c6f6b8" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockIssuedDuringPeriodValueNewIssues"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_e05918ad-55c0-4bd0-95c7-81cc801e07ed" xlink:to="loc_us-gaap_StockIssuedDuringPeriodValueNewIssues_e75111ff-f402-4422-8097-da66d9c6f6b8" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue_8f079033-fadf-46a6-bc3e-76e5f0aed8c8" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockRepurchasedAndRetiredDuringPeriodValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_e05918ad-55c0-4bd0-95c7-81cc801e07ed" xlink:to="loc_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue_8f079033-fadf-46a6-bc3e-76e5f0aed8c8" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_034940cd-e026-487d-8d30-bb9504745aca" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_e05918ad-55c0-4bd0-95c7-81cc801e07ed" xlink:to="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_034940cd-e026-487d-8d30-bb9504745aca" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss_43fd943c-43a2-4ef0-aa7d-14417129b2d3" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ProfitLoss"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_e05918ad-55c0-4bd0-95c7-81cc801e07ed" xlink:to="loc_us-gaap_ProfitLoss_43fd943c-43a2-4ef0-aa7d-14417129b2d3" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAttributableToRedeemableNoncontrollingInterest_eafa55b9-d0d8-43b5-962c-32fe75649b3a" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetIncomeLossAttributableToRedeemableNoncontrollingInterest"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_e05918ad-55c0-4bd0-95c7-81cc801e07ed" xlink:to="loc_us-gaap_NetIncomeLossAttributableToRedeemableNoncontrollingInterest_eafa55b9-d0d8-43b5-962c-32fe75649b3a" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity_f5643bde-0810-40d5-be87-4df8dcd2a7cd" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockholdersEquity"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/OrganizationDetails" xlink:type="simple" xlink:href="hg-20240930.xsd#OrganizationDetails"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/OrganizationDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_b6a7a14e-46d6-45e4-98f3-8c9b66cfe322" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEquityMethodInvestmentsTable_33dd8daf-338a-46b4-958b-e58cefe1cc76" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_b6a7a14e-46d6-45e4-98f3-8c9b66cfe322" xlink:to="loc_us-gaap_ScheduleOfEquityMethodInvestmentsTable_33dd8daf-338a-46b4-958b-e58cefe1cc76" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_00d8ec37-9202-4d43-b644-995aeca6eb29" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsTable_33dd8daf-338a-46b4-958b-e58cefe1cc76" xlink:to="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_00d8ec37-9202-4d43-b644-995aeca6eb29" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain_00d8ec37-9202-4d43-b644-995aeca6eb29_default" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_EquityMethodInvesteeNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_00d8ec37-9202-4d43-b644-995aeca6eb29" xlink:to="loc_srt_EquityMethodInvesteeNameDomain_00d8ec37-9202-4d43-b644-995aeca6eb29_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain_c58ff088-6879-4c74-8a50-b7a85ea03e83" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_EquityMethodInvesteeNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_00d8ec37-9202-4d43-b644-995aeca6eb29" xlink:to="loc_srt_EquityMethodInvesteeNameDomain_c58ff088-6879-4c74-8a50-b7a85ea03e83" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_TwoSigmaHamiltonFundLLCMember_a6516fa4-9f7c-4511-accd-0160201b9d7a" xlink:href="hg-20240930.xsd#hg_TwoSigmaHamiltonFundLLCMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_EquityMethodInvesteeNameDomain_c58ff088-6879-4c74-8a50-b7a85ea03e83" xlink:to="loc_hg_TwoSigmaHamiltonFundLLCMember_a6516fa4-9f7c-4511-accd-0160201b9d7a" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LegalEntityAxis_6e7866fc-18e2-4d8b-b10a-604a929c15c0" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_LegalEntityAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsTable_33dd8daf-338a-46b4-958b-e58cefe1cc76" xlink:to="loc_dei_LegalEntityAxis_6e7866fc-18e2-4d8b-b10a-604a929c15c0" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain_6e7866fc-18e2-4d8b-b10a-604a929c15c0_default" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_dei_LegalEntityAxis_6e7866fc-18e2-4d8b-b10a-604a929c15c0" xlink:to="loc_dei_EntityDomain_6e7866fc-18e2-4d8b-b10a-604a929c15c0_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain_c20accf0-39c5-4fbf-95bb-f143b333f533" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_dei_LegalEntityAxis_6e7866fc-18e2-4d8b-b10a-604a929c15c0" xlink:to="loc_dei_EntityDomain_c20accf0-39c5-4fbf-95bb-f143b333f533" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_HamiltonReMember_1565fc80-9a01-42a8-b505-794952afdb5a" xlink:href="hg-20240930.xsd#hg_HamiltonReMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_dei_EntityDomain_c20accf0-39c5-4fbf-95bb-f143b333f533" xlink:to="loc_hg_HamiltonReMember_1565fc80-9a01-42a8-b505-794952afdb5a" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_OtherCommitmentMinimumInvestmentCommitment_43114e89-4588-442b-bd94-5102d8cee925" xlink:href="hg-20240930.xsd#hg_OtherCommitmentMinimumInvestmentCommitment"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_b6a7a14e-46d6-45e4-98f3-8c9b66cfe322" xlink:to="loc_hg_OtherCommitmentMinimumInvestmentCommitment_43114e89-4588-442b-bd94-5102d8cee925" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_OtherCommitmentMinimumInvestmentCommitmentPercentageOfNetTangibleAssets_cbbf0381-5a0c-4baf-a202-4d2fa58d1b5b" xlink:href="hg-20240930.xsd#hg_OtherCommitmentMinimumInvestmentCommitmentPercentageOfNetTangibleAssets"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_b6a7a14e-46d6-45e4-98f3-8c9b66cfe322" xlink:to="loc_hg_OtherCommitmentMinimumInvestmentCommitmentPercentageOfNetTangibleAssets_cbbf0381-5a0c-4baf-a202-4d2fa58d1b5b" xlink:type="arc" order="1"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/InvestmentsScheduleofFixedMaturityandShortTermInvestmentsDetails" xlink:type="simple" xlink:href="hg-20240930.xsd#InvestmentsScheduleofFixedMaturityandShortTermInvestmentsDetails"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/InvestmentsScheduleofFixedMaturityandShortTermInvestmentsDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_10505acd-c0fb-4e91-8e1d-e94f42bf7b8e" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleTable_ba1e1097-da48-4c80-a3c9-4bae7f7816a3" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtSecuritiesAvailableForSaleTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_10505acd-c0fb-4e91-8e1d-e94f42bf7b8e" xlink:to="loc_us-gaap_DebtSecuritiesAvailableForSaleTable_ba1e1097-da48-4c80-a3c9-4bae7f7816a3" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis_295c77d3-b852-44f3-b0dd-e6ba0fb9a1a8" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinancialInstrumentAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleTable_ba1e1097-da48-4c80-a3c9-4bae7f7816a3" xlink:to="loc_us-gaap_FinancialInstrumentAxis_295c77d3-b852-44f3-b0dd-e6ba0fb9a1a8" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_295c77d3-b852-44f3-b0dd-e6ba0fb9a1a8_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_FinancialInstrumentAxis_295c77d3-b852-44f3-b0dd-e6ba0fb9a1a8" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_295c77d3-b852-44f3-b0dd-e6ba0fb9a1a8_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_293911ec-511f-4871-8046-449e3f16c27b" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_FinancialInstrumentAxis_295c77d3-b852-44f3-b0dd-e6ba0fb9a1a8" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_293911ec-511f-4871-8046-449e3f16c27b" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FixedMaturitiesMember_67ddc77c-de45-467a-81ce-27d4793e1cfb" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FixedMaturitiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_293911ec-511f-4871-8046-449e3f16c27b" xlink:to="loc_us-gaap_FixedMaturitiesMember_67ddc77c-de45-467a-81ce-27d4793e1cfb" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USTreasuryAndGovernmentMember_6eb9492c-0abf-441d-a994-a71e48c8251e" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_USTreasuryAndGovernmentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FixedMaturitiesMember_67ddc77c-de45-467a-81ce-27d4793e1cfb" xlink:to="loc_us-gaap_USTreasuryAndGovernmentMember_6eb9492c-0abf-441d-a994-a71e48c8251e" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USStatesAndPoliticalSubdivisionsMember_f8f06010-5eee-45e8-804d-eaaf6c3c247b" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_USStatesAndPoliticalSubdivisionsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FixedMaturitiesMember_67ddc77c-de45-467a-81ce-27d4793e1cfb" xlink:to="loc_us-gaap_USStatesAndPoliticalSubdivisionsMember_f8f06010-5eee-45e8-804d-eaaf6c3c247b" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignGovernmentDebtSecuritiesMember_21b12eac-cb97-431d-a837-58c5bde048ee" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ForeignGovernmentDebtSecuritiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FixedMaturitiesMember_67ddc77c-de45-467a-81ce-27d4793e1cfb" xlink:to="loc_us-gaap_ForeignGovernmentDebtSecuritiesMember_21b12eac-cb97-431d-a837-58c5bde048ee" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CorporateDebtSecuritiesMember_348585a8-daaf-436f-b958-a4e805f2a88e" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CorporateDebtSecuritiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FixedMaturitiesMember_67ddc77c-de45-467a-81ce-27d4793e1cfb" xlink:to="loc_us-gaap_CorporateDebtSecuritiesMember_348585a8-daaf-436f-b958-a4e805f2a88e" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember_11a3e3ac-a06c-4f20-b5af-81f9a0d94ca0" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FixedMaturitiesMember_67ddc77c-de45-467a-81ce-27d4793e1cfb" xlink:to="loc_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember_11a3e3ac-a06c-4f20-b5af-81f9a0d94ca0" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageBackedSecuritiesIssuedByPrivateEnterprisesMember_07dc490c-a5e0-46b0-abc0-8c1f76406cdf" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_MortgageBackedSecuritiesIssuedByPrivateEnterprisesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FixedMaturitiesMember_67ddc77c-de45-467a-81ce-27d4793e1cfb" xlink:to="loc_us-gaap_MortgageBackedSecuritiesIssuedByPrivateEnterprisesMember_07dc490c-a5e0-46b0-abc0-8c1f76406cdf" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommercialMortgageBackedSecuritiesMember_abeeb9df-e8ba-4c53-bc22-5a741d46b59f" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommercialMortgageBackedSecuritiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FixedMaturitiesMember_67ddc77c-de45-467a-81ce-27d4793e1cfb" xlink:to="loc_us-gaap_CommercialMortgageBackedSecuritiesMember_abeeb9df-e8ba-4c53-bc22-5a741d46b59f" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_OtherAssetBackedSecuritiesMember_b7803e0a-b45c-4728-8d1e-1a12b6d609d1" xlink:href="hg-20240930.xsd#hg_OtherAssetBackedSecuritiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FixedMaturitiesMember_67ddc77c-de45-467a-81ce-27d4793e1cfb" xlink:to="loc_hg_OtherAssetBackedSecuritiesMember_b7803e0a-b45c-4728-8d1e-1a12b6d609d1" xlink:type="arc" order="8"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortTermInvestmentsMember_5ca587f8-448d-4372-aa52-7ff6eb8d000e" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShortTermInvestmentsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_293911ec-511f-4871-8046-449e3f16c27b" xlink:to="loc_us-gaap_ShortTermInvestmentsMember_5ca587f8-448d-4372-aa52-7ff6eb8d000e" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradingSecuritiesDebtAmortizedCost_3821018c-93a0-4e79-a021-0cb7cc1a301d" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TradingSecuritiesDebtAmortizedCost"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_10505acd-c0fb-4e91-8e1d-e94f42bf7b8e" xlink:to="loc_us-gaap_TradingSecuritiesDebtAmortizedCost_3821018c-93a0-4e79-a021-0cb7cc1a301d" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_DebtSecuritiesTradingAccumulatedGrossUnrealizedGainBeforeTax_b2c9227b-50ee-45cb-bc87-be8f205c68b5" xlink:href="hg-20240930.xsd#hg_DebtSecuritiesTradingAccumulatedGrossUnrealizedGainBeforeTax"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_10505acd-c0fb-4e91-8e1d-e94f42bf7b8e" xlink:to="loc_hg_DebtSecuritiesTradingAccumulatedGrossUnrealizedGainBeforeTax_b2c9227b-50ee-45cb-bc87-be8f205c68b5" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_DebtSecuritiesTradingAccumulatedGrossUnrealizedLossBeforeTax_57511dce-ee58-44e6-9296-e7cf1e7fa137" xlink:href="hg-20240930.xsd#hg_DebtSecuritiesTradingAccumulatedGrossUnrealizedLossBeforeTax"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_10505acd-c0fb-4e91-8e1d-e94f42bf7b8e" xlink:to="loc_hg_DebtSecuritiesTradingAccumulatedGrossUnrealizedLossBeforeTax_57511dce-ee58-44e6-9296-e7cf1e7fa137" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradingSecuritiesDebt_9ae155fc-5dab-42c2-bf11-4a5ed5b0d715" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TradingSecuritiesDebt"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_10505acd-c0fb-4e91-8e1d-e94f42bf7b8e" xlink:to="loc_us-gaap_TradingSecuritiesDebt_9ae155fc-5dab-42c2-bf11-4a5ed5b0d715" xlink:type="arc" order="3"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/InvestmentsScheduleofContractualMaturitiesofFixedMaturitySecuritiesDetails" xlink:type="simple" xlink:href="hg-20240930.xsd#InvestmentsScheduleofContractualMaturitiesofFixedMaturitySecuritiesDetails"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/InvestmentsScheduleofContractualMaturitiesofFixedMaturitySecuritiesDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfHeldToMaturitySecuritiesLineItems_867947be-fcaf-4034-8941-2cc061f24feb" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfHeldToMaturitySecuritiesLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfHeldToMaturitySecuritiesTable_f21116b6-203a-4e38-adfe-03894e70a2bc" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfHeldToMaturitySecuritiesTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ScheduleOfHeldToMaturitySecuritiesLineItems_867947be-fcaf-4034-8941-2cc061f24feb" xlink:to="loc_us-gaap_ScheduleOfHeldToMaturitySecuritiesTable_f21116b6-203a-4e38-adfe-03894e70a2bc" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis_fe564330-44a3-491f-a908-fc59f94b27d1" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinancialInstrumentAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfHeldToMaturitySecuritiesTable_f21116b6-203a-4e38-adfe-03894e70a2bc" xlink:to="loc_us-gaap_FinancialInstrumentAxis_fe564330-44a3-491f-a908-fc59f94b27d1" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_fe564330-44a3-491f-a908-fc59f94b27d1_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_FinancialInstrumentAxis_fe564330-44a3-491f-a908-fc59f94b27d1" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_fe564330-44a3-491f-a908-fc59f94b27d1_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_ed7d53d5-f33b-463f-adcc-97f912af8f71" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_FinancialInstrumentAxis_fe564330-44a3-491f-a908-fc59f94b27d1" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_ed7d53d5-f33b-463f-adcc-97f912af8f71" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FixedMaturitiesMember_7236541d-e66d-43fb-885d-2889055199ce" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FixedMaturitiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_ed7d53d5-f33b-463f-adcc-97f912af8f71" xlink:to="loc_us-gaap_FixedMaturitiesMember_7236541d-e66d-43fb-885d-2889055199ce" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_FixedMaturitiesExcludingMortgageBackedAndAssetBackedSecuritiesMember_a4f590c3-f3cb-421a-a570-58ea516f0666" xlink:href="hg-20240930.xsd#hg_FixedMaturitiesExcludingMortgageBackedAndAssetBackedSecuritiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FixedMaturitiesMember_7236541d-e66d-43fb-885d-2889055199ce" xlink:to="loc_hg_FixedMaturitiesExcludingMortgageBackedAndAssetBackedSecuritiesMember_a4f590c3-f3cb-421a-a570-58ea516f0666" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageBackedSecuritiesMember_debae4d4-d7bb-4c0b-8f6e-2cfde8b9b0ec" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_MortgageBackedSecuritiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FixedMaturitiesMember_7236541d-e66d-43fb-885d-2889055199ce" xlink:to="loc_us-gaap_MortgageBackedSecuritiesMember_debae4d4-d7bb-4c0b-8f6e-2cfde8b9b0ec" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetBackedSecuritiesSecuritizedLoansAndReceivablesMember_3944ce02-508f-4253-b47d-9de3d000d448" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AssetBackedSecuritiesSecuritizedLoansAndReceivablesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FixedMaturitiesMember_7236541d-e66d-43fb-885d-2889055199ce" xlink:to="loc_us-gaap_AssetBackedSecuritiesSecuritizedLoansAndReceivablesMember_3944ce02-508f-4253-b47d-9de3d000d448" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract_38ad2e7b-83eb-4229-ab71-5ee42a98f7b0" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfHeldToMaturitySecuritiesLineItems_867947be-fcaf-4034-8941-2cc061f24feb" xlink:to="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract_38ad2e7b-83eb-4229-ab71-5ee42a98f7b0" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_DebtSecuritiesTradingAmortizedCostMaturityAllocatedAndSingleMaturityDateYearOne_8cb12a7a-1dae-485c-9293-de14cf45664e" xlink:href="hg-20240930.xsd#hg_DebtSecuritiesTradingAmortizedCostMaturityAllocatedAndSingleMaturityDateYearOne"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract_38ad2e7b-83eb-4229-ab71-5ee42a98f7b0" xlink:to="loc_hg_DebtSecuritiesTradingAmortizedCostMaturityAllocatedAndSingleMaturityDateYearOne_8cb12a7a-1dae-485c-9293-de14cf45664e" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_DebtSecuritiesTradingAmortizedCostMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughFive_ce206c71-4919-41df-b2af-aba36d429741" xlink:href="hg-20240930.xsd#hg_DebtSecuritiesTradingAmortizedCostMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughFive"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract_38ad2e7b-83eb-4229-ab71-5ee42a98f7b0" xlink:to="loc_hg_DebtSecuritiesTradingAmortizedCostMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughFive_ce206c71-4919-41df-b2af-aba36d429741" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_DebtSecuritiesTradingAmortizedCostMaturityAllocatedAndSingleMaturityDateAfterYear5Through10_882ae69e-5ac5-454b-ac09-4fbc449008e3" xlink:href="hg-20240930.xsd#hg_DebtSecuritiesTradingAmortizedCostMaturityAllocatedAndSingleMaturityDateAfterYear5Through10"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract_38ad2e7b-83eb-4229-ab71-5ee42a98f7b0" xlink:to="loc_hg_DebtSecuritiesTradingAmortizedCostMaturityAllocatedAndSingleMaturityDateAfterYear5Through10_882ae69e-5ac5-454b-ac09-4fbc449008e3" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_DebtSecuritiesTradingAmortizedCostMaturityAllocatedAndSingleMaturityDateAfterYear10_6eef9dc0-0842-494a-bc16-551e9ffa4a14" xlink:href="hg-20240930.xsd#hg_DebtSecuritiesTradingAmortizedCostMaturityAllocatedAndSingleMaturityDateAfterYear10"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract_38ad2e7b-83eb-4229-ab71-5ee42a98f7b0" xlink:to="loc_hg_DebtSecuritiesTradingAmortizedCostMaturityAllocatedAndSingleMaturityDateAfterYear10_6eef9dc0-0842-494a-bc16-551e9ffa4a14" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_DebtSecuritiesTradingMaturityWithoutSingleMaturityDateAmortizedCost_60b905c5-d572-4eca-b3a4-696be92ed4bb" xlink:href="hg-20240930.xsd#hg_DebtSecuritiesTradingMaturityWithoutSingleMaturityDateAmortizedCost"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract_38ad2e7b-83eb-4229-ab71-5ee42a98f7b0" xlink:to="loc_hg_DebtSecuritiesTradingMaturityWithoutSingleMaturityDateAmortizedCost_60b905c5-d572-4eca-b3a4-696be92ed4bb" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradingSecuritiesDebtAmortizedCost_f1ed6d39-fad5-4570-84d7-44013dc68a6d" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TradingSecuritiesDebtAmortizedCost"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract_38ad2e7b-83eb-4229-ab71-5ee42a98f7b0" xlink:to="loc_us-gaap_TradingSecuritiesDebtAmortizedCost_f1ed6d39-fad5-4570-84d7-44013dc68a6d" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract_4e129699-9120-4942-93fd-7cbc49d7f622" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfHeldToMaturitySecuritiesLineItems_867947be-fcaf-4034-8941-2cc061f24feb" xlink:to="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract_4e129699-9120-4942-93fd-7cbc49d7f622" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_DebtSecuritiesTradingFairValueMaturityAllocatedAndSingleMaturityDateYearOne_eee052e4-172e-4c54-bbcf-e0e452092a76" xlink:href="hg-20240930.xsd#hg_DebtSecuritiesTradingFairValueMaturityAllocatedAndSingleMaturityDateYearOne"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract_4e129699-9120-4942-93fd-7cbc49d7f622" xlink:to="loc_hg_DebtSecuritiesTradingFairValueMaturityAllocatedAndSingleMaturityDateYearOne_eee052e4-172e-4c54-bbcf-e0e452092a76" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_DebtSecuritiesTradingFairValueMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughFive_fe1cd5f1-3e9c-40e7-a08d-45b5cd0201df" xlink:href="hg-20240930.xsd#hg_DebtSecuritiesTradingFairValueMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughFive"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract_4e129699-9120-4942-93fd-7cbc49d7f622" xlink:to="loc_hg_DebtSecuritiesTradingFairValueMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughFive_fe1cd5f1-3e9c-40e7-a08d-45b5cd0201df" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_DebtSecuritiesTradingFairValueMaturityAllocatedAndSingleMaturityDateAfterYear5Through10_7a39cb33-ff5f-420a-af4e-7b611ba51868" xlink:href="hg-20240930.xsd#hg_DebtSecuritiesTradingFairValueMaturityAllocatedAndSingleMaturityDateAfterYear5Through10"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract_4e129699-9120-4942-93fd-7cbc49d7f622" xlink:to="loc_hg_DebtSecuritiesTradingFairValueMaturityAllocatedAndSingleMaturityDateAfterYear5Through10_7a39cb33-ff5f-420a-af4e-7b611ba51868" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_DebtSecuritiesTradingFairValueMaturityAllocatedAndSingleMaturityDateAfterYear10_f661b446-4117-450f-b037-151fa072b53d" xlink:href="hg-20240930.xsd#hg_DebtSecuritiesTradingFairValueMaturityAllocatedAndSingleMaturityDateAfterYear10"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract_4e129699-9120-4942-93fd-7cbc49d7f622" xlink:to="loc_hg_DebtSecuritiesTradingFairValueMaturityAllocatedAndSingleMaturityDateAfterYear10_f661b446-4117-450f-b037-151fa072b53d" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_DebtSecuritiesTradingMaturityWithoutSingleMaturityDateFairValue_3eadd8d0-0067-4090-9773-f99421cde0a7" xlink:href="hg-20240930.xsd#hg_DebtSecuritiesTradingMaturityWithoutSingleMaturityDateFairValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract_4e129699-9120-4942-93fd-7cbc49d7f622" xlink:to="loc_hg_DebtSecuritiesTradingMaturityWithoutSingleMaturityDateFairValue_3eadd8d0-0067-4090-9773-f99421cde0a7" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradingSecuritiesDebt_e8863662-ef45-4e45-83c1-b7d51734c7f6" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TradingSecuritiesDebt"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract_4e129699-9120-4942-93fd-7cbc49d7f622" xlink:to="loc_us-gaap_TradingSecuritiesDebt_e8863662-ef45-4e45-83c1-b7d51734c7f6" xlink:type="arc" order="6"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/InvestmentsScheduleofInvestmentsinTwoSigmaFundsDetails" xlink:type="simple" xlink:href="hg-20240930.xsd#InvestmentsScheduleofInvestmentsinTwoSigmaFundsDetails"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/InvestmentsScheduleofInvestmentsinTwoSigmaFundsDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MarketableSecuritiesLineItems_503c1b9f-7278-429d-a31f-ac1eff3fe9f8" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_MarketableSecuritiesLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MarketableSecuritiesTable_41f1e64d-9487-4d93-9ccb-f8c802c2ee89" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_MarketableSecuritiesTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_MarketableSecuritiesLineItems_503c1b9f-7278-429d-a31f-ac1eff3fe9f8" xlink:to="loc_us-gaap_MarketableSecuritiesTable_41f1e64d-9487-4d93-9ccb-f8c802c2ee89" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_90816a5d-48a5-41f2-a78a-28ab0acc8183" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_MarketableSecuritiesTable_41f1e64d-9487-4d93-9ccb-f8c802c2ee89" xlink:to="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_90816a5d-48a5-41f2-a78a-28ab0acc8183" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain_90816a5d-48a5-41f2-a78a-28ab0acc8183_default" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_EquityMethodInvesteeNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_90816a5d-48a5-41f2-a78a-28ab0acc8183" xlink:to="loc_srt_EquityMethodInvesteeNameDomain_90816a5d-48a5-41f2-a78a-28ab0acc8183_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain_06570b02-8b13-4bec-bd16-0da7c8a9e455" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_EquityMethodInvesteeNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_90816a5d-48a5-41f2-a78a-28ab0acc8183" xlink:to="loc_srt_EquityMethodInvesteeNameDomain_06570b02-8b13-4bec-bd16-0da7c8a9e455" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_TwoSigmaFundsMember_fdb95df1-8fbd-4fc9-b9ca-d7c2cd3d22aa" xlink:href="hg-20240930.xsd#hg_TwoSigmaFundsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_EquityMethodInvesteeNameDomain_06570b02-8b13-4bec-bd16-0da7c8a9e455" xlink:to="loc_hg_TwoSigmaFundsMember_fdb95df1-8fbd-4fc9-b9ca-d7c2cd3d22aa" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_TwoSigmaFuturesPortfolioLLCFTVMember_a41b1277-03bf-4624-962b-b2d426e87909" xlink:href="hg-20240930.xsd#hg_TwoSigmaFuturesPortfolioLLCFTVMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_hg_TwoSigmaFundsMember_fdb95df1-8fbd-4fc9-b9ca-d7c2cd3d22aa" xlink:to="loc_hg_TwoSigmaFuturesPortfolioLLCFTVMember_a41b1277-03bf-4624-962b-b2d426e87909" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_TwoSigmaSpectrumPortfolioLLCSTVMember_9bc6bffe-c094-4e04-8cef-ba3902a66801" xlink:href="hg-20240930.xsd#hg_TwoSigmaSpectrumPortfolioLLCSTVMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_hg_TwoSigmaFundsMember_fdb95df1-8fbd-4fc9-b9ca-d7c2cd3d22aa" xlink:to="loc_hg_TwoSigmaSpectrumPortfolioLLCSTVMember_9bc6bffe-c094-4e04-8cef-ba3902a66801" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_TwoSigmaEquitySpectrumPortfolioLLCESTVMember_e4b978bd-7000-4048-b382-57fcc23621bc" xlink:href="hg-20240930.xsd#hg_TwoSigmaEquitySpectrumPortfolioLLCESTVMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_hg_TwoSigmaFundsMember_fdb95df1-8fbd-4fc9-b9ca-d7c2cd3d22aa" xlink:to="loc_hg_TwoSigmaEquitySpectrumPortfolioLLCESTVMember_e4b978bd-7000-4048-b382-57fcc23621bc" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentOwnedAtCost_0b4f29ce-bbcf-40ca-8f6a-14e7c63de587" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InvestmentOwnedAtCost"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_MarketableSecuritiesLineItems_503c1b9f-7278-429d-a31f-ac1eff3fe9f8" xlink:to="loc_us-gaap_InvestmentOwnedAtCost_0b4f29ce-bbcf-40ca-8f6a-14e7c63de587" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_InvestmentOwnedAccumulatedGrossUnrealizedGainLossBeforeTax_5c95c0c3-47d2-4b7e-a374-6d78f1e56e80" xlink:href="hg-20240930.xsd#hg_InvestmentOwnedAccumulatedGrossUnrealizedGainLossBeforeTax"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_MarketableSecuritiesLineItems_503c1b9f-7278-429d-a31f-ac1eff3fe9f8" xlink:to="loc_hg_InvestmentOwnedAccumulatedGrossUnrealizedGainLossBeforeTax_5c95c0c3-47d2-4b7e-a374-6d78f1e56e80" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AlternativeInvestment_58a81382-44ca-4d6f-9e11-5039a25402bb" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AlternativeInvestment"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_MarketableSecuritiesLineItems_503c1b9f-7278-429d-a31f-ac1eff3fe9f8" xlink:to="loc_us-gaap_AlternativeInvestment_58a81382-44ca-4d6f-9e11-5039a25402bb" xlink:type="arc" order="2"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/InvestmentsNarrativeDetails" xlink:type="simple" xlink:href="hg-20240930.xsd#InvestmentsNarrativeDetails"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/InvestmentsNarrativeDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems_fa649a2e-e90d-4e99-92d7-7a3650485cf8" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable_058ef70d-404d-4505-b295-1e22f9c53528" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems_fa649a2e-e90d-4e99-92d7-7a3650485cf8" xlink:to="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable_058ef70d-404d-4505-b295-1e22f9c53528" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_cbd8fedc-a49a-4476-80cc-42b7ec785fec" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable_058ef70d-404d-4505-b295-1e22f9c53528" xlink:to="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_cbd8fedc-a49a-4476-80cc-42b7ec785fec" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain_cbd8fedc-a49a-4476-80cc-42b7ec785fec_default" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_EquityMethodInvesteeNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_cbd8fedc-a49a-4476-80cc-42b7ec785fec" xlink:to="loc_srt_EquityMethodInvesteeNameDomain_cbd8fedc-a49a-4476-80cc-42b7ec785fec_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain_058c1e6a-86fa-4a89-862b-8d08d9f050f1" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_EquityMethodInvesteeNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_cbd8fedc-a49a-4476-80cc-42b7ec785fec" xlink:to="loc_srt_EquityMethodInvesteeNameDomain_058c1e6a-86fa-4a89-862b-8d08d9f050f1" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_TwoSigmaFuturesPortfolioLLCFTVMember_2ad929b4-30d0-4773-8ebc-511412245f81" xlink:href="hg-20240930.xsd#hg_TwoSigmaFuturesPortfolioLLCFTVMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_EquityMethodInvesteeNameDomain_058c1e6a-86fa-4a89-862b-8d08d9f050f1" xlink:to="loc_hg_TwoSigmaFuturesPortfolioLLCFTVMember_2ad929b4-30d0-4773-8ebc-511412245f81" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_TwoSigmaSpectrumPortfolioLLCSTVMember_ce471b9a-21fb-4de1-8ed0-d57d65a831b0" xlink:href="hg-20240930.xsd#hg_TwoSigmaSpectrumPortfolioLLCSTVMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_EquityMethodInvesteeNameDomain_058c1e6a-86fa-4a89-862b-8d08d9f050f1" xlink:to="loc_hg_TwoSigmaSpectrumPortfolioLLCSTVMember_ce471b9a-21fb-4de1-8ed0-d57d65a831b0" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_TwoSigmaEquitySpectrumPortfolioLLCESTVMember_dddfe65b-194a-4bde-bda8-65a3da1ded32" xlink:href="hg-20240930.xsd#hg_TwoSigmaEquitySpectrumPortfolioLLCESTVMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_EquityMethodInvesteeNameDomain_058c1e6a-86fa-4a89-862b-8d08d9f050f1" xlink:to="loc_hg_TwoSigmaEquitySpectrumPortfolioLLCESTVMember_dddfe65b-194a-4bde-bda8-65a3da1ded32" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_TwoSigmaHamiltonFundLLCMember_f4d232ce-8a2d-4584-977f-71fa9ad808f2" xlink:href="hg-20240930.xsd#hg_TwoSigmaHamiltonFundLLCMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_EquityMethodInvesteeNameDomain_058c1e6a-86fa-4a89-862b-8d08d9f050f1" xlink:to="loc_hg_TwoSigmaHamiltonFundLLCMember_f4d232ce-8a2d-4584-977f-71fa9ad808f2" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesAxis_50e1177d-8eb3-4284-96e7-5e10b6e6bdbe" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ConsolidatedEntitiesAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable_058ef70d-404d-4505-b295-1e22f9c53528" xlink:to="loc_srt_ConsolidatedEntitiesAxis_50e1177d-8eb3-4284-96e7-5e10b6e6bdbe" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesDomain_50e1177d-8eb3-4284-96e7-5e10b6e6bdbe_default" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ConsolidatedEntitiesDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_ConsolidatedEntitiesAxis_50e1177d-8eb3-4284-96e7-5e10b6e6bdbe" xlink:to="loc_srt_ConsolidatedEntitiesDomain_50e1177d-8eb3-4284-96e7-5e10b6e6bdbe_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesDomain_9de2bba2-c04d-4570-ba40-3ce6bb2d44c5" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ConsolidatedEntitiesDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_ConsolidatedEntitiesAxis_50e1177d-8eb3-4284-96e7-5e10b6e6bdbe" xlink:to="loc_srt_ConsolidatedEntitiesDomain_9de2bba2-c04d-4570-ba40-3ce6bb2d44c5" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_2079c6ff-f7ad-4310-a211-7dc67828ddd1" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_VariableInterestEntityPrimaryBeneficiaryMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ConsolidatedEntitiesDomain_9de2bba2-c04d-4570-ba40-3ce6bb2d44c5" xlink:to="loc_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_2079c6ff-f7ad-4310-a211-7dc67828ddd1" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PledgingPurposeAxis_be552807-74a8-44af-8e86-29d57b268197" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PledgingPurposeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable_058ef70d-404d-4505-b295-1e22f9c53528" xlink:to="loc_us-gaap_PledgingPurposeAxis_be552807-74a8-44af-8e86-29d57b268197" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PledgingPurposeDomain_be552807-74a8-44af-8e86-29d57b268197_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PledgingPurposeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_PledgingPurposeAxis_be552807-74a8-44af-8e86-29d57b268197" xlink:to="loc_us-gaap_PledgingPurposeDomain_be552807-74a8-44af-8e86-29d57b268197_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PledgingPurposeDomain_c0390e7b-3f52-4c7c-8c81-5734c91dbf31" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PledgingPurposeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_PledgingPurposeAxis_be552807-74a8-44af-8e86-29d57b268197" xlink:to="loc_us-gaap_PledgingPurposeDomain_c0390e7b-3f52-4c7c-8c81-5734c91dbf31" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_CapitalRequirementsMember_73522247-4c28-4871-91d7-970895cb1dbe" xlink:href="hg-20240930.xsd#hg_CapitalRequirementsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_PledgingPurposeDomain_c0390e7b-3f52-4c7c-8c81-5734c91dbf31" xlink:to="loc_hg_CapitalRequirementsMember_73522247-4c28-4871-91d7-970895cb1dbe" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_TrustAccountsMember_2ded8f4c-ca04-4d98-a496-ddd3aa7eb590" xlink:href="hg-20240930.xsd#hg_TrustAccountsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_PledgingPurposeDomain_c0390e7b-3f52-4c7c-8c81-5734c91dbf31" xlink:to="loc_hg_TrustAccountsMember_2ded8f4c-ca04-4d98-a496-ddd3aa7eb590" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_UnderwritingObligationsMember_79eeb6fb-f87b-4c60-8744-789dfef42529" xlink:href="hg-20240930.xsd#hg_UnderwritingObligationsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_PledgingPurposeDomain_c0390e7b-3f52-4c7c-8c81-5734c91dbf31" xlink:to="loc_hg_UnderwritingObligationsMember_79eeb6fb-f87b-4c60-8744-789dfef42529" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_EscrowFundsMember_e37df491-975f-4d63-86c9-9b1f76aaff85" xlink:href="hg-20240930.xsd#hg_EscrowFundsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_PledgingPurposeDomain_c0390e7b-3f52-4c7c-8c81-5734c91dbf31" xlink:to="loc_hg_EscrowFundsMember_e37df491-975f-4d63-86c9-9b1f76aaff85" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PledgedStatusAxis_28e790a7-9a5a-4509-b55c-145d629f4a6d" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PledgedStatusAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable_058ef70d-404d-4505-b295-1e22f9c53528" xlink:to="loc_us-gaap_PledgedStatusAxis_28e790a7-9a5a-4509-b55c-145d629f4a6d" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PledgedStatusDomain_28e790a7-9a5a-4509-b55c-145d629f4a6d_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PledgedStatusDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_PledgedStatusAxis_28e790a7-9a5a-4509-b55c-145d629f4a6d" xlink:to="loc_us-gaap_PledgedStatusDomain_28e790a7-9a5a-4509-b55c-145d629f4a6d_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PledgedStatusDomain_93390f03-dee7-441c-8d15-74bb8cf46619" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PledgedStatusDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_PledgedStatusAxis_28e790a7-9a5a-4509-b55c-145d629f4a6d" xlink:to="loc_us-gaap_PledgedStatusDomain_93390f03-dee7-441c-8d15-74bb8cf46619" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetPledgedAsCollateralMember_32eb255d-98dc-4a87-b6ab-f8aad5b52ebe" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AssetPledgedAsCollateralMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_PledgedStatusDomain_93390f03-dee7-441c-8d15-74bb8cf46619" xlink:to="loc_us-gaap_AssetPledgedAsCollateralMember_32eb255d-98dc-4a87-b6ab-f8aad5b52ebe" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LegalEntityAxis_f4eda096-d5b3-4ad1-a4ab-89015814acc6" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_LegalEntityAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable_058ef70d-404d-4505-b295-1e22f9c53528" xlink:to="loc_dei_LegalEntityAxis_f4eda096-d5b3-4ad1-a4ab-89015814acc6" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain_f4eda096-d5b3-4ad1-a4ab-89015814acc6_default" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_dei_LegalEntityAxis_f4eda096-d5b3-4ad1-a4ab-89015814acc6" xlink:to="loc_dei_EntityDomain_f4eda096-d5b3-4ad1-a4ab-89015814acc6_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain_6e614cdc-b409-43a9-adc5-12b1ed4ef92a" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_dei_LegalEntityAxis_f4eda096-d5b3-4ad1-a4ab-89015814acc6" xlink:to="loc_dei_EntityDomain_6e614cdc-b409-43a9-adc5-12b1ed4ef92a" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_HamiltonReMember_b0b97162-cf99-494d-a575-016172b2aa1f" xlink:href="hg-20240930.xsd#hg_HamiltonReMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_dei_EntityDomain_6e614cdc-b409-43a9-adc5-12b1ed4ef92a" xlink:to="loc_hg_HamiltonReMember_b0b97162-cf99-494d-a575-016172b2aa1f" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_AlternativeInvestmentOwnershipPercentage_aedfcfdc-ca41-4e6f-8574-24d949da3a9f" xlink:href="hg-20240930.xsd#hg_AlternativeInvestmentOwnershipPercentage"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems_fa649a2e-e90d-4e99-92d7-7a3650485cf8" xlink:to="loc_hg_AlternativeInvestmentOwnershipPercentage_aedfcfdc-ca41-4e6f-8574-24d949da3a9f" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ManagementAndServiceFeesRate_ddabee37-9484-4ece-9456-4d5044f0eb8a" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ManagementAndServiceFeesRate"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems_fa649a2e-e90d-4e99-92d7-7a3650485cf8" xlink:to="loc_us-gaap_ManagementAndServiceFeesRate_ddabee37-9484-4ece-9456-4d5044f0eb8a" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ManagementFeeExpense_95092139-e1d1-471a-a5aa-62e43313d94a" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ManagementFeeExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems_fa649a2e-e90d-4e99-92d7-7a3650485cf8" xlink:to="loc_us-gaap_ManagementFeeExpense_95092139-e1d1-471a-a5aa-62e43313d94a" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ManagementAndServiceFeesIncentiveRate_677a7047-268e-4437-91b4-0a0bb9d66e1e" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ManagementAndServiceFeesIncentiveRate"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems_fa649a2e-e90d-4e99-92d7-7a3650485cf8" xlink:to="loc_us-gaap_ManagementAndServiceFeesIncentiveRate_677a7047-268e-4437-91b4-0a0bb9d66e1e" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_ManagementAndServiceFeesIncentiveRatePercentageReduction_792e5d52-0ff2-43fb-a478-01756376a64c" xlink:href="hg-20240930.xsd#hg_ManagementAndServiceFeesIncentiveRatePercentageReduction"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems_fa649a2e-e90d-4e99-92d7-7a3650485cf8" xlink:to="loc_hg_ManagementAndServiceFeesIncentiveRatePercentageReduction_792e5d52-0ff2-43fb-a478-01756376a64c" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_ManagementAndServicesFeesIncentiveRateCumulativeNetProfitsRecoveryHurdlePercentage_d3532a17-7d5f-48fa-9a18-9c97ab114cbf" xlink:href="hg-20240930.xsd#hg_ManagementAndServicesFeesIncentiveRateCumulativeNetProfitsRecoveryHurdlePercentage"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems_fa649a2e-e90d-4e99-92d7-7a3650485cf8" xlink:to="loc_hg_ManagementAndServicesFeesIncentiveRateCumulativeNetProfitsRecoveryHurdlePercentage_d3532a17-7d5f-48fa-9a18-9c97ab114cbf" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_ManagementAndServicesFeesIncentiveRateExcessProfitsPercentage_79e94fd7-1d57-41fa-b0b8-697a3cc12ca1" xlink:href="hg-20240930.xsd#hg_ManagementAndServicesFeesIncentiveRateExcessProfitsPercentage"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems_fa649a2e-e90d-4e99-92d7-7a3650485cf8" xlink:to="loc_hg_ManagementAndServicesFeesIncentiveRateExcessProfitsPercentage_79e94fd7-1d57-41fa-b0b8-697a3cc12ca1" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_ManagementAndServicesFeesIncentiveRateNetProfitsHurdlePercentage_7e047155-348f-4270-a4f5-f3ea7330e4d4" xlink:href="hg-20240930.xsd#hg_ManagementAndServicesFeesIncentiveRateNetProfitsHurdlePercentage"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems_fa649a2e-e90d-4e99-92d7-7a3650485cf8" xlink:to="loc_hg_ManagementAndServicesFeesIncentiveRateNetProfitsHurdlePercentage_7e047155-348f-4270-a4f5-f3ea7330e4d4" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_IncentiveFeeExpenseIncome_d1bba1b3-f2f1-4001-8a4e-cff791e97b07" xlink:href="hg-20240930.xsd#hg_IncentiveFeeExpenseIncome"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems_fa649a2e-e90d-4e99-92d7-7a3650485cf8" xlink:to="loc_hg_IncentiveFeeExpenseIncome_d1bba1b3-f2f1-4001-8a4e-cff791e97b07" xlink:type="arc" order="8"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_OtherCommitmentMinimumInvestmentCommitment_84973904-2929-4227-986f-e5c863f747f4" xlink:href="hg-20240930.xsd#hg_OtherCommitmentMinimumInvestmentCommitment"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems_fa649a2e-e90d-4e99-92d7-7a3650485cf8" xlink:to="loc_hg_OtherCommitmentMinimumInvestmentCommitment_84973904-2929-4227-986f-e5c863f747f4" xlink:type="arc" order="9"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_OtherCommitmentMinimumInvestmentCommitmentPercentageOfNetTangibleAssets_a60a8245-497c-4c3e-8934-7a11fcfb1ca0" xlink:href="hg-20240930.xsd#hg_OtherCommitmentMinimumInvestmentCommitmentPercentageOfNetTangibleAssets"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems_fa649a2e-e90d-4e99-92d7-7a3650485cf8" xlink:to="loc_hg_OtherCommitmentMinimumInvestmentCommitmentPercentageOfNetTangibleAssets_a60a8245-497c-4c3e-8934-7a11fcfb1ca0" xlink:type="arc" order="10"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_OtherCommitmentsTerm_9227d69b-f0e1-4f39-a617-84c45274278e" xlink:href="hg-20240930.xsd#hg_OtherCommitmentsTerm"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems_fa649a2e-e90d-4e99-92d7-7a3650485cf8" xlink:to="loc_hg_OtherCommitmentsTerm_9227d69b-f0e1-4f39-a617-84c45274278e" xlink:type="arc" order="11"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_OtherCommitmentsCapitalAccountWithdrawalNumberOfCalendarDaysPriorToMonthEnd_1daea288-9e01-4a8e-b1fd-9d08d900f6a3" xlink:href="hg-20240930.xsd#hg_OtherCommitmentsCapitalAccountWithdrawalNumberOfCalendarDaysPriorToMonthEnd"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems_fa649a2e-e90d-4e99-92d7-7a3650485cf8" xlink:to="loc_hg_OtherCommitmentsCapitalAccountWithdrawalNumberOfCalendarDaysPriorToMonthEnd_1daea288-9e01-4a8e-b1fd-9d08d900f6a3" xlink:type="arc" order="12"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_OtherCommitmentsCapitalAccountWithdrawalDailyLiquidityNumberOfBusinessDaysWrittenNotice_2d16f8fb-84d4-4a76-85ae-edbd4d7b9055" xlink:href="hg-20240930.xsd#hg_OtherCommitmentsCapitalAccountWithdrawalDailyLiquidityNumberOfBusinessDaysWrittenNotice"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems_fa649a2e-e90d-4e99-92d7-7a3650485cf8" xlink:to="loc_hg_OtherCommitmentsCapitalAccountWithdrawalDailyLiquidityNumberOfBusinessDaysWrittenNotice_2d16f8fb-84d4-4a76-85ae-edbd4d7b9055" xlink:type="arc" order="13"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsFairValueDisclosure_31d3f12f-c065-44a3-bbcd-f0c15205a3da" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InvestmentsFairValueDisclosure"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems_fa649a2e-e90d-4e99-92d7-7a3650485cf8" xlink:to="loc_us-gaap_InvestmentsFairValueDisclosure_31d3f12f-c065-44a3-bbcd-f0c15205a3da" xlink:type="arc" order="14"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCashAndCashEquivalents_c8225942-bed9-4aa3-9114-dd0cb4a02c7f" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RestrictedCashAndCashEquivalents"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems_fa649a2e-e90d-4e99-92d7-7a3650485cf8" xlink:to="loc_us-gaap_RestrictedCashAndCashEquivalents_c8225942-bed9-4aa3-9114-dd0cb4a02c7f" xlink:type="arc" order="15"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_60ef252a-378f-4ecc-8492-afdef8e647c7" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems_fa649a2e-e90d-4e99-92d7-7a3650485cf8" xlink:to="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_60ef252a-378f-4ecc-8492-afdef8e647c7" xlink:type="arc" order="16"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue_ceea218b-c150-41b0-9b3e-141bc896710c" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems_fa649a2e-e90d-4e99-92d7-7a3650485cf8" xlink:to="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue_ceea218b-c150-41b0-9b3e-141bc896710c" xlink:type="arc" order="17"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/InvestmentsScheduleofCertainInvestmentsDetails" xlink:type="simple" xlink:href="hg-20240930.xsd#InvestmentsScheduleofCertainInvestmentsDetails"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/InvestmentsScheduleofCertainInvestmentsDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems_ae49b01f-8082-462c-b66b-36a0273f272d" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable_ae510fe5-83be-489b-bcd3-02d51de6a2cb" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems_ae49b01f-8082-462c-b66b-36a0273f272d" xlink:to="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable_ae510fe5-83be-489b-bcd3-02d51de6a2cb" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis_5478b04c-77e9-4422-abe9-bd7ac0996b63" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinancialInstrumentAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable_ae510fe5-83be-489b-bcd3-02d51de6a2cb" xlink:to="loc_us-gaap_FinancialInstrumentAxis_5478b04c-77e9-4422-abe9-bd7ac0996b63" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_5478b04c-77e9-4422-abe9-bd7ac0996b63_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_FinancialInstrumentAxis_5478b04c-77e9-4422-abe9-bd7ac0996b63" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_5478b04c-77e9-4422-abe9-bd7ac0996b63_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_98116ab2-4d0d-44a9-8d7f-929a3af9b9df" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_FinancialInstrumentAxis_5478b04c-77e9-4422-abe9-bd7ac0996b63" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_98116ab2-4d0d-44a9-8d7f-929a3af9b9df" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_StateStreetTreasuryObligationsMoneyMarketFundMember_022db67b-3ac4-4b50-84a2-c440505f37d1" xlink:href="hg-20240930.xsd#hg_StateStreetTreasuryObligationsMoneyMarketFundMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_98116ab2-4d0d-44a9-8d7f-929a3af9b9df" xlink:to="loc_hg_StateStreetTreasuryObligationsMoneyMarketFundMember_022db67b-3ac4-4b50-84a2-c440505f37d1" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_USTreasurySecuritiesMaturing20242044Member_f79fa2b2-908e-4306-a48a-991f641521d2" xlink:href="hg-20240930.xsd#hg_USTreasurySecuritiesMaturing20242044Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_98116ab2-4d0d-44a9-8d7f-929a3af9b9df" xlink:to="loc_hg_USTreasurySecuritiesMaturing20242044Member_f79fa2b2-908e-4306-a48a-991f641521d2" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_StateStreetInstitutionalTreasuryPlusMoneyMarketFundMember_74570e97-891b-4c59-85ac-d179f0a30917" xlink:href="hg-20240930.xsd#hg_StateStreetInstitutionalTreasuryPlusMoneyMarketFundMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_98116ab2-4d0d-44a9-8d7f-929a3af9b9df" xlink:to="loc_hg_StateStreetInstitutionalTreasuryPlusMoneyMarketFundMember_74570e97-891b-4c59-85ac-d179f0a30917" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_U.S.TreasurySecuritiesMaturing20262054Member_73b54fe4-353f-49c0-b46d-82e583bd4118" xlink:href="hg-20240930.xsd#hg_U.S.TreasurySecuritiesMaturing20262054Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_98116ab2-4d0d-44a9-8d7f-929a3af9b9df" xlink:to="loc_hg_U.S.TreasurySecuritiesMaturing20262054Member_73b54fe4-353f-49c0-b46d-82e583bd4118" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByBenchmarkAxis_6e3dd9e4-8bfe-4f1d-bb69-131a5cd11117" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskByBenchmarkAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable_ae510fe5-83be-489b-bcd3-02d51de6a2cb" xlink:to="loc_us-gaap_ConcentrationRiskByBenchmarkAxis_6e3dd9e4-8bfe-4f1d-bb69-131a5cd11117" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskBenchmarkDomain_6e3dd9e4-8bfe-4f1d-bb69-131a5cd11117_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskBenchmarkDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_ConcentrationRiskByBenchmarkAxis_6e3dd9e4-8bfe-4f1d-bb69-131a5cd11117" xlink:to="loc_us-gaap_ConcentrationRiskBenchmarkDomain_6e3dd9e4-8bfe-4f1d-bb69-131a5cd11117_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskBenchmarkDomain_ea744f6a-03e5-40a1-9dae-73d8e3ced363" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskBenchmarkDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_ConcentrationRiskByBenchmarkAxis_6e3dd9e4-8bfe-4f1d-bb69-131a5cd11117" xlink:to="loc_us-gaap_ConcentrationRiskBenchmarkDomain_ea744f6a-03e5-40a1-9dae-73d8e3ced363" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityTotalMember_b0651070-2351-4e7a-a8d1-7c51bd6cc280" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockholdersEquityTotalMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ConcentrationRiskBenchmarkDomain_ea744f6a-03e5-40a1-9dae-73d8e3ced363" xlink:to="loc_us-gaap_StockholdersEquityTotalMember_b0651070-2351-4e7a-a8d1-7c51bd6cc280" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByTypeAxis_14c1fe2b-4d3a-45ca-a5e6-26d8206964c1" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskByTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable_ae510fe5-83be-489b-bcd3-02d51de6a2cb" xlink:to="loc_us-gaap_ConcentrationRiskByTypeAxis_14c1fe2b-4d3a-45ca-a5e6-26d8206964c1" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskTypeDomain_14c1fe2b-4d3a-45ca-a5e6-26d8206964c1_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_ConcentrationRiskByTypeAxis_14c1fe2b-4d3a-45ca-a5e6-26d8206964c1" xlink:to="loc_us-gaap_ConcentrationRiskTypeDomain_14c1fe2b-4d3a-45ca-a5e6-26d8206964c1_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskTypeDomain_ac92051c-4bcd-4750-972d-a79728e2f116" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_ConcentrationRiskByTypeAxis_14c1fe2b-4d3a-45ca-a5e6-26d8206964c1" xlink:to="loc_us-gaap_ConcentrationRiskTypeDomain_ac92051c-4bcd-4750-972d-a79728e2f116" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_InvestmentTypeConcentrationRiskMember_e8abe540-184a-4e2f-b4c0-c2a12dd79330" xlink:href="hg-20240930.xsd#hg_InvestmentTypeConcentrationRiskMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ConcentrationRiskTypeDomain_ac92051c-4bcd-4750-972d-a79728e2f116" xlink:to="loc_hg_InvestmentTypeConcentrationRiskMember_e8abe540-184a-4e2f-b4c0-c2a12dd79330" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesAxis_9f0f4d28-0cc0-452c-a0ae-3541a9b27e9a" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ConsolidatedEntitiesAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable_ae510fe5-83be-489b-bcd3-02d51de6a2cb" xlink:to="loc_srt_ConsolidatedEntitiesAxis_9f0f4d28-0cc0-452c-a0ae-3541a9b27e9a" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesDomain_9f0f4d28-0cc0-452c-a0ae-3541a9b27e9a_default" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ConsolidatedEntitiesDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_ConsolidatedEntitiesAxis_9f0f4d28-0cc0-452c-a0ae-3541a9b27e9a" xlink:to="loc_srt_ConsolidatedEntitiesDomain_9f0f4d28-0cc0-452c-a0ae-3541a9b27e9a_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesDomain_45f18b82-8604-4f31-98f6-d23a0fb386a7" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ConsolidatedEntitiesDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_ConsolidatedEntitiesAxis_9f0f4d28-0cc0-452c-a0ae-3541a9b27e9a" xlink:to="loc_srt_ConsolidatedEntitiesDomain_45f18b82-8604-4f31-98f6-d23a0fb386a7" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_fc2b5df8-d4fa-4ffe-aa6c-9f3229b1d12f" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_VariableInterestEntityPrimaryBeneficiaryMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ConsolidatedEntitiesDomain_45f18b82-8604-4f31-98f6-d23a0fb386a7" xlink:to="loc_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_fc2b5df8-d4fa-4ffe-aa6c-9f3229b1d12f" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PositionAxis_912031a8-a5cc-4ac0-b4aa-a26a5a40605e" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PositionAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable_ae510fe5-83be-489b-bcd3-02d51de6a2cb" xlink:to="loc_us-gaap_PositionAxis_912031a8-a5cc-4ac0-b4aa-a26a5a40605e" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PositionDomain_912031a8-a5cc-4ac0-b4aa-a26a5a40605e_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PositionDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_PositionAxis_912031a8-a5cc-4ac0-b4aa-a26a5a40605e" xlink:to="loc_us-gaap_PositionDomain_912031a8-a5cc-4ac0-b4aa-a26a5a40605e_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PositionDomain_f9a2ade2-ec81-4f8a-bb74-f73c4ce48d3a" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PositionDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_PositionAxis_912031a8-a5cc-4ac0-b4aa-a26a5a40605e" xlink:to="loc_us-gaap_PositionDomain_f9a2ade2-ec81-4f8a-bb74-f73c4ce48d3a" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongMember_38345d63-497e-4c8c-9753-21fe75891f7d" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LongMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_PositionDomain_f9a2ade2-ec81-4f8a-bb74-f73c4ce48d3a" xlink:to="loc_us-gaap_LongMember_38345d63-497e-4c8c-9753-21fe75891f7d" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortMember_16116346-4f28-4c1d-b99f-1513b7e32687" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShortMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_PositionDomain_f9a2ade2-ec81-4f8a-bb74-f73c4ce48d3a" xlink:to="loc_us-gaap_ShortMember_16116346-4f28-4c1d-b99f-1513b7e32687" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentOwnedBalanceShares_e3955345-ad8c-471b-92db-f62b7a14762f" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InvestmentOwnedBalanceShares"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems_ae49b01f-8082-462c-b66b-36a0273f272d" xlink:to="loc_us-gaap_InvestmentOwnedBalanceShares_e3955345-ad8c-471b-92db-f62b7a14762f" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AlternativeInvestment_8f219d2b-fde1-4856-95ef-0b8ec0fc8326" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AlternativeInvestment"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems_ae49b01f-8082-462c-b66b-36a0273f272d" xlink:to="loc_us-gaap_AlternativeInvestment_8f219d2b-fde1-4856-95ef-0b8ec0fc8326" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskPercentage1_5e5491b9-bce7-4f59-8416-5f15ee02c35f" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskPercentage1"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryLineItems_ae49b01f-8082-462c-b66b-36a0273f272d" xlink:to="loc_us-gaap_ConcentrationRiskPercentage1_5e5491b9-bce7-4f59-8416-5f15ee02c35f" xlink:type="arc" order="2"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/InvestmentsScheduleofRealizedandUnrealizedGainsLossesonInvestmentsandNetInvestmentIncomeLossDetails" xlink:type="simple" xlink:href="hg-20240930.xsd#InvestmentsScheduleofRealizedandUnrealizedGainsLossesonInvestmentsandNetInvestmentIncomeLossDetails"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/InvestmentsScheduleofRealizedandUnrealizedGainsLossesonInvestmentsandNetInvestmentIncomeLossDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_e8b78707-634d-44f8-acf7-56fb3a5b4bf9" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleTable_2ecd660d-d211-4664-a6d9-a7dbe4ca24d5" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtSecuritiesAvailableForSaleTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_e8b78707-634d-44f8-acf7-56fb3a5b4bf9" xlink:to="loc_us-gaap_DebtSecuritiesAvailableForSaleTable_2ecd660d-d211-4664-a6d9-a7dbe4ca24d5" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeAxis_582a4331-244d-4a02-a9b4-b39d3d79c2f8" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InvestmentTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleTable_2ecd660d-d211-4664-a6d9-a7dbe4ca24d5" xlink:to="loc_us-gaap_InvestmentTypeAxis_582a4331-244d-4a02-a9b4-b39d3d79c2f8" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeCategorizationMember_582a4331-244d-4a02-a9b4-b39d3d79c2f8_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InvestmentTypeCategorizationMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_InvestmentTypeAxis_582a4331-244d-4a02-a9b4-b39d3d79c2f8" xlink:to="loc_us-gaap_InvestmentTypeCategorizationMember_582a4331-244d-4a02-a9b4-b39d3d79c2f8_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeCategorizationMember_6d794aa3-8e0e-423b-befd-6093a31c6024" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InvestmentTypeCategorizationMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_InvestmentTypeAxis_582a4331-244d-4a02-a9b4-b39d3d79c2f8" xlink:to="loc_us-gaap_InvestmentTypeCategorizationMember_6d794aa3-8e0e-423b-befd-6093a31c6024" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FixedMaturitiesMember_63d2263d-a949-4a4a-96ab-760d867b4c68" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FixedMaturitiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_6d794aa3-8e0e-423b-befd-6093a31c6024" xlink:to="loc_us-gaap_FixedMaturitiesMember_63d2263d-a949-4a4a-96ab-760d867b4c68" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortTermInvestmentsMember_86207c92-e26c-4af0-a225-9423337b2b93" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShortTermInvestmentsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_6d794aa3-8e0e-423b-befd-6093a31c6024" xlink:to="loc_us-gaap_ShortTermInvestmentsMember_86207c92-e26c-4af0-a225-9423337b2b93" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_TSHamiltonFundMember_fe04e820-d489-4bc5-8c61-2a34e0278f10" xlink:href="hg-20240930.xsd#hg_TSHamiltonFundMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_6d794aa3-8e0e-423b-befd-6093a31c6024" xlink:to="loc_hg_TSHamiltonFundMember_fe04e820-d489-4bc5-8c61-2a34e0278f10" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsMember_9e54526f-c3e6-49b9-a963-5d17e82d2315" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CashAndCashEquivalentsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_6d794aa3-8e0e-423b-befd-6093a31c6024" xlink:to="loc_us-gaap_CashAndCashEquivalentsMember_9e54526f-c3e6-49b9-a963-5d17e82d2315" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_OtherInvestmentsNettingMember_92682b20-15b1-421f-9d99-03930bf93531" xlink:href="hg-20240930.xsd#hg_OtherInvestmentsNettingMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_6d794aa3-8e0e-423b-befd-6093a31c6024" xlink:to="loc_hg_OtherInvestmentsNettingMember_92682b20-15b1-421f-9d99-03930bf93531" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_FixedMaturitiesAndShortTermInvestmentsMember_2da64ae8-2172-4d7e-9fec-be4cc30b96a7" xlink:href="hg-20240930.xsd#hg_FixedMaturitiesAndShortTermInvestmentsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_6d794aa3-8e0e-423b-befd-6093a31c6024" xlink:to="loc_hg_FixedMaturitiesAndShortTermInvestmentsMember_2da64ae8-2172-4d7e-9fec-be4cc30b96a7" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherInvestmentsMember_232ab68c-72c4-4308-a657-4b71a722fba8" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherInvestmentsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember_6d794aa3-8e0e-423b-befd-6093a31c6024" xlink:to="loc_us-gaap_OtherInvestmentsMember_232ab68c-72c4-4308-a657-4b71a722fba8" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_NetRealizedAndUnrealizedGainsLossesOnInvestmentsAbstract_a25cb996-b1f5-4afc-bbe4-409524761647" xlink:href="hg-20240930.xsd#hg_NetRealizedAndUnrealizedGainsLossesOnInvestmentsAbstract"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_e8b78707-634d-44f8-acf7-56fb3a5b4bf9" xlink:to="loc_hg_NetRealizedAndUnrealizedGainsLossesOnInvestmentsAbstract_a25cb996-b1f5-4afc-bbe4-409524761647" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealizedInvestmentGainsLosses_8d54bb64-b9ef-4f41-89cf-50f6d329c861" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RealizedInvestmentGainsLosses"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_hg_NetRealizedAndUnrealizedGainsLossesOnInvestmentsAbstract_a25cb996-b1f5-4afc-bbe4-409524761647" xlink:to="loc_us-gaap_RealizedInvestmentGainsLosses_8d54bb64-b9ef-4f41-89cf-50f6d329c861" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrealizedGainLossOnInvestments_194a6c67-d323-4efe-b237-d989ca1dbb99" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_UnrealizedGainLossOnInvestments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_hg_NetRealizedAndUnrealizedGainsLossesOnInvestmentsAbstract_a25cb996-b1f5-4afc-bbe4-409524761647" xlink:to="loc_us-gaap_UnrealizedGainLossOnInvestments_194a6c67-d323-4efe-b237-d989ca1dbb99" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnInvestments_2d69477b-49cc-46e3-a4fd-bb8092fde8ae" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GainLossOnInvestments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_hg_NetRealizedAndUnrealizedGainsLossesOnInvestmentsAbstract_a25cb996-b1f5-4afc-bbe4-409524761647" xlink:to="loc_us-gaap_GainLossOnInvestments_2d69477b-49cc-46e3-a4fd-bb8092fde8ae" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetInvestmentIncomeAbstract_68c6595e-7980-467d-8a90-b0e9aaacd633" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetInvestmentIncomeAbstract"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_hg_NetRealizedAndUnrealizedGainsLossesOnInvestmentsAbstract_a25cb996-b1f5-4afc-bbe4-409524761647" xlink:to="loc_us-gaap_NetInvestmentIncomeAbstract_68c6595e-7980-467d-8a90-b0e9aaacd633" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeInterestAndDividend_8d9b6b16-8229-4ea7-9d04-1b40e718f810" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InvestmentIncomeInterestAndDividend"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_NetInvestmentIncomeAbstract_68c6595e-7980-467d-8a90-b0e9aaacd633" xlink:to="loc_us-gaap_InvestmentIncomeInterestAndDividend_8d9b6b16-8229-4ea7-9d04-1b40e718f810" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ManagementFeeExpense_6a0448ea-4fbd-4861-9c29-9132ce646b2b" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ManagementFeeExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_NetInvestmentIncomeAbstract_68c6595e-7980-467d-8a90-b0e9aaacd633" xlink:to="loc_us-gaap_ManagementFeeExpense_6a0448ea-4fbd-4861-9c29-9132ce646b2b" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeInvestmentExpense_187b3211-eecc-476d-bd08-790bd77e69b7" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InvestmentIncomeInvestmentExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_NetInvestmentIncomeAbstract_68c6595e-7980-467d-8a90-b0e9aaacd633" xlink:to="loc_us-gaap_InvestmentIncomeInvestmentExpense_187b3211-eecc-476d-bd08-790bd77e69b7" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeNet_3e065476-b212-44a5-b548-9ed7c69d6337" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InvestmentIncomeNet"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_NetInvestmentIncomeAbstract_68c6595e-7980-467d-8a90-b0e9aaacd633" xlink:to="loc_us-gaap_InvestmentIncomeNet_3e065476-b212-44a5-b548-9ed7c69d6337" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_GainLossOnInvestmentsAndNetInvestmentIncome_1476e693-ad2a-4b49-a270-cc347a4e5a05" xlink:href="hg-20240930.xsd#hg_GainLossOnInvestmentsAndNetInvestmentIncome"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_hg_NetRealizedAndUnrealizedGainsLossesOnInvestmentsAbstract_a25cb996-b1f5-4afc-bbe4-409524761647" xlink:to="loc_hg_GainLossOnInvestmentsAndNetInvestmentIncome_1476e693-ad2a-4b49-a270-cc347a4e5a05" xlink:type="arc" order="5"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/FairValueDetails" xlink:type="simple" xlink:href="hg-20240930.xsd#FairValueDetails"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/FairValueDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosureAssetAndLiabilityNotMeasuredAtFairValueLineItems_41aa98c9-3425-41bf-8976-a74d6ea6fa31" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueDisclosureAssetAndLiabilityNotMeasuredAtFairValueLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosureOfAssetAndLiabilityNotMeasuredAtFairValueTable_37f3ad32-1cd5-4e8d-b398-d004a7ebfccf" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueDisclosureOfAssetAndLiabilityNotMeasuredAtFairValueTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_FairValueDisclosureAssetAndLiabilityNotMeasuredAtFairValueLineItems_41aa98c9-3425-41bf-8976-a74d6ea6fa31" xlink:to="loc_us-gaap_FairValueDisclosureOfAssetAndLiabilityNotMeasuredAtFairValueTable_37f3ad32-1cd5-4e8d-b398-d004a7ebfccf" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis_5d790bd9-0a08-43c1-8ede-bcb32104db15" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_FairValueDisclosureOfAssetAndLiabilityNotMeasuredAtFairValueTable_37f3ad32-1cd5-4e8d-b398-d004a7ebfccf" xlink:to="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis_5d790bd9-0a08-43c1-8ede-bcb32104db15" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_5d790bd9-0a08-43c1-8ede-bcb32104db15_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis_5d790bd9-0a08-43c1-8ede-bcb32104db15" xlink:to="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_5d790bd9-0a08-43c1-8ede-bcb32104db15_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_e2c00a9b-db84-43d4-957f-9c0bd143767d" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis_5d790bd9-0a08-43c1-8ede-bcb32104db15" xlink:to="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_e2c00a9b-db84-43d4-957f-9c0bd143767d" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel1Member_9eb1876b-cbe7-4a7b-8c04-d2ccb29cc253" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueInputsLevel1Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_e2c00a9b-db84-43d4-957f-9c0bd143767d" xlink:to="loc_us-gaap_FairValueInputsLevel1Member_9eb1876b-cbe7-4a7b-8c04-d2ccb29cc253" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel2Member_104c8cfc-f0f8-42bd-b924-98461bcc2c23" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueInputsLevel2Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_e2c00a9b-db84-43d4-957f-9c0bd143767d" xlink:to="loc_us-gaap_FairValueInputsLevel2Member_104c8cfc-f0f8-42bd-b924-98461bcc2c23" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel3Member_89a2ee4c-3ba9-4247-8ac4-131774c96b12" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueInputsLevel3Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_e2c00a9b-db84-43d4-957f-9c0bd143767d" xlink:to="loc_us-gaap_FairValueInputsLevel3Member_89a2ee4c-3ba9-4247-8ac4-131774c96b12" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis_621a5ef4-fdc4-4ced-8970-cf0446afea51" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinancialInstrumentAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_FairValueDisclosureOfAssetAndLiabilityNotMeasuredAtFairValueTable_37f3ad32-1cd5-4e8d-b398-d004a7ebfccf" xlink:to="loc_us-gaap_FinancialInstrumentAxis_621a5ef4-fdc4-4ced-8970-cf0446afea51" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_621a5ef4-fdc4-4ced-8970-cf0446afea51_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_FinancialInstrumentAxis_621a5ef4-fdc4-4ced-8970-cf0446afea51" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_621a5ef4-fdc4-4ced-8970-cf0446afea51_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_0cfe4ad2-4c7b-4e7e-b04e-5e0928eac957" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_FinancialInstrumentAxis_621a5ef4-fdc4-4ced-8970-cf0446afea51" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_0cfe4ad2-4c7b-4e7e-b04e-5e0928eac957" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FixedMaturitiesMember_ce8824fb-e23f-447b-a98c-8b0d17117ceb" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FixedMaturitiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_0cfe4ad2-4c7b-4e7e-b04e-5e0928eac957" xlink:to="loc_us-gaap_FixedMaturitiesMember_ce8824fb-e23f-447b-a98c-8b0d17117ceb" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USTreasuryAndGovernmentMember_8bf1743d-51b5-4b0f-a8df-08f1f1add8af" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_USTreasuryAndGovernmentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FixedMaturitiesMember_ce8824fb-e23f-447b-a98c-8b0d17117ceb" xlink:to="loc_us-gaap_USTreasuryAndGovernmentMember_8bf1743d-51b5-4b0f-a8df-08f1f1add8af" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USStatesAndPoliticalSubdivisionsMember_78624df0-272b-4926-8bd7-8ba5292bdda0" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_USStatesAndPoliticalSubdivisionsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FixedMaturitiesMember_ce8824fb-e23f-447b-a98c-8b0d17117ceb" xlink:to="loc_us-gaap_USStatesAndPoliticalSubdivisionsMember_78624df0-272b-4926-8bd7-8ba5292bdda0" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignGovernmentDebtSecuritiesMember_3ef1cd8e-b341-4a7c-a6cb-a76a344a1338" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ForeignGovernmentDebtSecuritiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FixedMaturitiesMember_ce8824fb-e23f-447b-a98c-8b0d17117ceb" xlink:to="loc_us-gaap_ForeignGovernmentDebtSecuritiesMember_3ef1cd8e-b341-4a7c-a6cb-a76a344a1338" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CorporateDebtSecuritiesMember_d0433638-d0f0-457b-8ab9-08d4f994f68a" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CorporateDebtSecuritiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FixedMaturitiesMember_ce8824fb-e23f-447b-a98c-8b0d17117ceb" xlink:to="loc_us-gaap_CorporateDebtSecuritiesMember_d0433638-d0f0-457b-8ab9-08d4f994f68a" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember_5f65e713-cd33-453a-8dae-c607751114f8" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FixedMaturitiesMember_ce8824fb-e23f-447b-a98c-8b0d17117ceb" xlink:to="loc_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember_5f65e713-cd33-453a-8dae-c607751114f8" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageBackedSecuritiesIssuedByPrivateEnterprisesMember_bfb6d14f-7194-41e9-9dc6-1f78a07b408e" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_MortgageBackedSecuritiesIssuedByPrivateEnterprisesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FixedMaturitiesMember_ce8824fb-e23f-447b-a98c-8b0d17117ceb" xlink:to="loc_us-gaap_MortgageBackedSecuritiesIssuedByPrivateEnterprisesMember_bfb6d14f-7194-41e9-9dc6-1f78a07b408e" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommercialMortgageBackedSecuritiesMember_7ab69144-4dc5-466a-8288-6a3d8a23e9d7" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommercialMortgageBackedSecuritiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FixedMaturitiesMember_ce8824fb-e23f-447b-a98c-8b0d17117ceb" xlink:to="loc_us-gaap_CommercialMortgageBackedSecuritiesMember_7ab69144-4dc5-466a-8288-6a3d8a23e9d7" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_OtherAssetBackedSecuritiesMember_38a442eb-2e71-4731-9906-a8ee089293dd" xlink:href="hg-20240930.xsd#hg_OtherAssetBackedSecuritiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FixedMaturitiesMember_ce8824fb-e23f-447b-a98c-8b0d17117ceb" xlink:to="loc_hg_OtherAssetBackedSecuritiesMember_38a442eb-2e71-4731-9906-a8ee089293dd" xlink:type="arc" order="8"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortTermInvestmentsMember_cdba5360-e84a-44b9-a089-7ff7e34025d8" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShortTermInvestmentsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_0cfe4ad2-4c7b-4e7e-b04e-5e0928eac957" xlink:to="loc_us-gaap_ShortTermInvestmentsMember_cdba5360-e84a-44b9-a089-7ff7e34025d8" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradingSecuritiesDebt_8271f05c-e497-414d-bdf0-7c28bef1ed5b" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TradingSecuritiesDebt"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FairValueDisclosureAssetAndLiabilityNotMeasuredAtFairValueLineItems_41aa98c9-3425-41bf-8976-a74d6ea6fa31" xlink:to="loc_us-gaap_TradingSecuritiesDebt_8271f05c-e497-414d-bdf0-7c28bef1ed5b" xlink:type="arc" order="0"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/VariableInterestEntitiesScheduleofActivityintheNonControllingInterestDetails" xlink:type="simple" xlink:href="hg-20240930.xsd#VariableInterestEntitiesScheduleofActivityintheNonControllingInterestDetails"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/VariableInterestEntitiesScheduleofActivityintheNonControllingInterestDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CollaborativeArrangementsAndNoncollaborativeArrangementTransactionsLineItems_d859d8d1-62b9-4bb5-a7b7-fc415a765e72" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CollaborativeArrangementsAndNoncollaborativeArrangementTransactionsLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfCollaborativeArrangementsAndNoncollaborativeArrangementTransactionsTable_c004cc40-438f-4b67-a1b9-7d9d1ef6f913" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfCollaborativeArrangementsAndNoncollaborativeArrangementTransactionsTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_CollaborativeArrangementsAndNoncollaborativeArrangementTransactionsLineItems_d859d8d1-62b9-4bb5-a7b7-fc415a765e72" xlink:to="loc_us-gaap_ScheduleOfCollaborativeArrangementsAndNoncollaborativeArrangementTransactionsTable_c004cc40-438f-4b67-a1b9-7d9d1ef6f913" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesAxis_6d7c686e-69ce-4747-b143-14d11572d5f1" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ConsolidatedEntitiesAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfCollaborativeArrangementsAndNoncollaborativeArrangementTransactionsTable_c004cc40-438f-4b67-a1b9-7d9d1ef6f913" xlink:to="loc_srt_ConsolidatedEntitiesAxis_6d7c686e-69ce-4747-b143-14d11572d5f1" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesDomain_6d7c686e-69ce-4747-b143-14d11572d5f1_default" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ConsolidatedEntitiesDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_ConsolidatedEntitiesAxis_6d7c686e-69ce-4747-b143-14d11572d5f1" xlink:to="loc_srt_ConsolidatedEntitiesDomain_6d7c686e-69ce-4747-b143-14d11572d5f1_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesDomain_2b458d0b-c2b2-447e-a8d8-b0a1cb5fb00c" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ConsolidatedEntitiesDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_ConsolidatedEntitiesAxis_6d7c686e-69ce-4747-b143-14d11572d5f1" xlink:to="loc_srt_ConsolidatedEntitiesDomain_2b458d0b-c2b2-447e-a8d8-b0a1cb5fb00c" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_3e2bd34d-aaf8-41c5-b89b-2253653814dd" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_VariableInterestEntityPrimaryBeneficiaryMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ConsolidatedEntitiesDomain_2b458d0b-c2b2-447e-a8d8-b0a1cb5fb00c" xlink:to="loc_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_3e2bd34d-aaf8-41c5-b89b-2253653814dd" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MovementInMinorityInterestRollForward_c7f570b4-a56b-40e8-8d02-be4407643149" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_MovementInMinorityInterestRollForward"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CollaborativeArrangementsAndNoncollaborativeArrangementTransactionsLineItems_d859d8d1-62b9-4bb5-a7b7-fc415a765e72" xlink:to="loc_us-gaap_MovementInMinorityInterestRollForward_c7f570b4-a56b-40e8-8d02-be4407643149" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_4d0e2fcd-6a89-4c5a-965b-6c901437dd4c" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_MovementInMinorityInterestRollForward_c7f570b4-a56b-40e8-8d02-be4407643149" xlink:to="loc_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_4d0e2fcd-6a89-4c5a-965b-6c901437dd4c" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders_0a2d862e-0880-4772-88b7-99a21fe06240" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_MovementInMinorityInterestRollForward_c7f570b4-a56b-40e8-8d02-be4407643149" xlink:to="loc_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders_0a2d862e-0880-4772-88b7-99a21fe06240" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_d121a3c5-87cc-4450-ba96-e28a36556a35" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetIncomeLossAttributableToNoncontrollingInterest"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_MovementInMinorityInterestRollForward_c7f570b4-a56b-40e8-8d02-be4407643149" xlink:to="loc_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_d121a3c5-87cc-4450-ba96-e28a36556a35" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_NoncontrollingInterestIncreaseDecreaseFromIncentiveAllocation_71461947-3ba5-491a-8602-7b31ba895f73" xlink:href="hg-20240930.xsd#hg_NoncontrollingInterestIncreaseDecreaseFromIncentiveAllocation"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_MovementInMinorityInterestRollForward_c7f570b4-a56b-40e8-8d02-be4407643149" xlink:to="loc_hg_NoncontrollingInterestIncreaseDecreaseFromIncentiveAllocation_71461947-3ba5-491a-8602-7b31ba895f73" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_6df94af2-4e37-44b4-b539-b8bcb23aecd3" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/VariableInterestEntitiesScheduleofTotalAssetsandTotalLiabilitiesofTSHamiltonFundDetails" xlink:type="simple" xlink:href="hg-20240930.xsd#VariableInterestEntitiesScheduleofTotalAssetsandTotalLiabilitiesofTSHamiltonFundDetails"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/VariableInterestEntitiesScheduleofTotalAssetsandTotalLiabilitiesofTSHamiltonFundDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityLineItems_ad02cf6d-fd73-4fa4-990f-33f96e35177d" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_VariableInterestEntityLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable_896d09cd-c9de-4913-8731-4a12130d6ccf" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfVariableInterestEntitiesTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_VariableInterestEntityLineItems_ad02cf6d-fd73-4fa4-990f-33f96e35177d" xlink:to="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable_896d09cd-c9de-4913-8731-4a12130d6ccf" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesAxis_0bb36f08-5f23-4d4b-b5a9-d76fcdae8a95" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ConsolidatedEntitiesAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable_896d09cd-c9de-4913-8731-4a12130d6ccf" xlink:to="loc_srt_ConsolidatedEntitiesAxis_0bb36f08-5f23-4d4b-b5a9-d76fcdae8a95" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesDomain_0bb36f08-5f23-4d4b-b5a9-d76fcdae8a95_default" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ConsolidatedEntitiesDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_ConsolidatedEntitiesAxis_0bb36f08-5f23-4d4b-b5a9-d76fcdae8a95" xlink:to="loc_srt_ConsolidatedEntitiesDomain_0bb36f08-5f23-4d4b-b5a9-d76fcdae8a95_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesDomain_32f5e823-0411-4772-83c0-a8b5b6a14901" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ConsolidatedEntitiesDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_ConsolidatedEntitiesAxis_0bb36f08-5f23-4d4b-b5a9-d76fcdae8a95" xlink:to="loc_srt_ConsolidatedEntitiesDomain_32f5e823-0411-4772-83c0-a8b5b6a14901" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_384a93df-a95c-40a2-9385-77c94d0951b3" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_VariableInterestEntityPrimaryBeneficiaryMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ConsolidatedEntitiesDomain_32f5e823-0411-4772-83c0-a8b5b6a14901" xlink:to="loc_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_384a93df-a95c-40a2-9385-77c94d0951b3" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis_35f98934-0787-4250-93fb-d3f084dc2372" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinancialInstrumentAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable_896d09cd-c9de-4913-8731-4a12130d6ccf" xlink:to="loc_us-gaap_FinancialInstrumentAxis_35f98934-0787-4250-93fb-d3f084dc2372" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_35f98934-0787-4250-93fb-d3f084dc2372_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_FinancialInstrumentAxis_35f98934-0787-4250-93fb-d3f084dc2372" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_35f98934-0787-4250-93fb-d3f084dc2372_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_86335386-8ed1-4ec5-b9a7-0967023489ff" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_FinancialInstrumentAxis_35f98934-0787-4250-93fb-d3f084dc2372" xlink:to="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_86335386-8ed1-4ec5-b9a7-0967023489ff" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortTermInvestmentsMember_76702e6b-6688-4f4d-8856-304e40c5b6bb" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShortTermInvestmentsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_86335386-8ed1-4ec5-b9a7-0967023489ff" xlink:to="loc_us-gaap_ShortTermInvestmentsMember_76702e6b-6688-4f4d-8856-304e40c5b6bb" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsAbstract_3c9bc8c4-eda9-4085-84d9-6aacc0bda449" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AssetsAbstract"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_VariableInterestEntityLineItems_ad02cf6d-fd73-4fa4-990f-33f96e35177d" xlink:to="loc_us-gaap_AssetsAbstract_3c9bc8c4-eda9-4085-84d9-6aacc0bda449" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue_d1c42eb6-90b1-4449-9d11-39ea9c30e40d" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AssetsAbstract_3c9bc8c4-eda9-4085-84d9-6aacc0bda449" xlink:to="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue_d1c42eb6-90b1-4449-9d11-39ea9c30e40d" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradingSecuritiesDebt_9532dbe1-647b-4adb-8576-b7d552d0f8f1" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TradingSecuritiesDebt"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AssetsAbstract_3c9bc8c4-eda9-4085-84d9-6aacc0bda449" xlink:to="loc_us-gaap_TradingSecuritiesDebt_9532dbe1-647b-4adb-8576-b7d552d0f8f1" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AlternativeInvestment_71552a8e-014b-4d86-850b-7cb99fa6dc11" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AlternativeInvestment"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AssetsAbstract_3c9bc8c4-eda9-4085-84d9-6aacc0bda449" xlink:to="loc_us-gaap_AlternativeInvestment_71552a8e-014b-4d86-850b-7cb99fa6dc11" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivablesFromBrokersDealersAndClearingOrganizations_7d3b64d8-1661-4780-8cbe-a5a1a001ffdc" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ReceivablesFromBrokersDealersAndClearingOrganizations"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AssetsAbstract_3c9bc8c4-eda9-4085-84d9-6aacc0bda449" xlink:to="loc_us-gaap_ReceivablesFromBrokersDealersAndClearingOrganizations_7d3b64d8-1661-4780-8cbe-a5a1a001ffdc" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendAndInterestReceivable_e8d8ea47-ed4e-4b53-a475-6c610b50f458" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DividendAndInterestReceivable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AssetsAbstract_3c9bc8c4-eda9-4085-84d9-6aacc0bda449" xlink:to="loc_us-gaap_DividendAndInterestReceivable_e8d8ea47-ed4e-4b53-a475-6c610b50f458" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets_9b89fc06-cf64-47ab-86c7-10ac4e1c98b9" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_Assets"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AssetsAbstract_3c9bc8c4-eda9-4085-84d9-6aacc0bda449" xlink:to="loc_us-gaap_Assets_9b89fc06-cf64-47ab-86c7-10ac4e1c98b9" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAbstract_29da48cb-e71a-4145-b7b9-d9ae58a646db" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LiabilitiesAbstract"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_VariableInterestEntityLineItems_ad02cf6d-fd73-4fa4-990f-33f96e35177d" xlink:to="loc_us-gaap_LiabilitiesAbstract_29da48cb-e71a-4145-b7b9-d9ae58a646db" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent_f19994f2-71fa-444a-8e68-fac859ab5a82" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilitiesAbstract_29da48cb-e71a-4145-b7b9-d9ae58a646db" xlink:to="loc_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent_f19994f2-71fa-444a-8e68-fac859ab5a82" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_WithdrawalPayable_7dc8384d-e4bc-4686-8235-6977123d0593" xlink:href="hg-20240930.xsd#hg_WithdrawalPayable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilitiesAbstract_29da48cb-e71a-4145-b7b9-d9ae58a646db" xlink:to="loc_hg_WithdrawalPayable_7dc8384d-e4bc-4686-8235-6977123d0593" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_PayablesToBrokerDealersAndClearingOrganizations_9b41384f-f2cc-44d5-ba58-4d883acae466" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_PayablesToBrokerDealersAndClearingOrganizations"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilitiesAbstract_29da48cb-e71a-4145-b7b9-d9ae58a646db" xlink:to="loc_srt_PayablesToBrokerDealersAndClearingOrganizations_9b41384f-f2cc-44d5-ba58-4d883acae466" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities_40934962-bbb9-4a6b-90c0-40e1bd62e72f" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_Liabilities"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilitiesAbstract_29da48cb-e71a-4145-b7b9-d9ae58a646db" xlink:to="loc_us-gaap_Liabilities_40934962-bbb9-4a6b-90c0-40e1bd62e72f" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_VariableInterestEntityNetAssetsLiabilities_8f980360-d8fd-4617-8624-0b91eb271a8f" xlink:href="hg-20240930.xsd#hg_VariableInterestEntityNetAssetsLiabilities"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_VariableInterestEntityLineItems_ad02cf6d-fd73-4fa4-990f-33f96e35177d" xlink:to="loc_hg_VariableInterestEntityNetAssetsLiabilities_8f980360-d8fd-4617-8624-0b91eb271a8f" xlink:type="arc" order="2"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/ValueAppreciationPoolDetails" xlink:type="simple" xlink:href="hg-20240930.xsd#ValueAppreciationPoolDetails"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/ValueAppreciationPoolDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems_1f896058-052c-46e6-98a3-318074affd10" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable_30dd4ce1-ffb0-455a-a877-4c5b962c8a84" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems_1f896058-052c-46e6-98a3-318074affd10" xlink:to="loc_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable_30dd4ce1-ffb0-455a-a877-4c5b962c8a84" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VestingAxis_68ba1063-d9d4-4da9-b550-7ee40ff2ba54" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_VestingAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable_30dd4ce1-ffb0-455a-a877-4c5b962c8a84" xlink:to="loc_us-gaap_VestingAxis_68ba1063-d9d4-4da9-b550-7ee40ff2ba54" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VestingDomain_68ba1063-d9d4-4da9-b550-7ee40ff2ba54_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_VestingDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_VestingAxis_68ba1063-d9d4-4da9-b550-7ee40ff2ba54" xlink:to="loc_us-gaap_VestingDomain_68ba1063-d9d4-4da9-b550-7ee40ff2ba54_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VestingDomain_0e86ec78-6f46-4a48-83e8-92ef729d91b9" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_VestingDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_VestingAxis_68ba1063-d9d4-4da9-b550-7ee40ff2ba54" xlink:to="loc_us-gaap_VestingDomain_0e86ec78-6f46-4a48-83e8-92ef729d91b9" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationAwardTrancheOneMember_4b72b37b-1980-40d0-ba17-d9ee59b236c8" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationAwardTrancheOneMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_VestingDomain_0e86ec78-6f46-4a48-83e8-92ef729d91b9" xlink:to="loc_us-gaap_ShareBasedCompensationAwardTrancheOneMember_4b72b37b-1980-40d0-ba17-d9ee59b236c8" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationAwardTrancheTwoMember_f1343dd3-4995-4cf7-ad62-c81d9c1ac805" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationAwardTrancheTwoMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_VestingDomain_0e86ec78-6f46-4a48-83e8-92ef729d91b9" xlink:to="loc_us-gaap_ShareBasedCompensationAwardTrancheTwoMember_f1343dd3-4995-4cf7-ad62-c81d9c1ac805" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AwardTypeAxis_2ce3e800-d5db-4ef2-8ebc-db04c450b614" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AwardTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable_30dd4ce1-ffb0-455a-a877-4c5b962c8a84" xlink:to="loc_us-gaap_AwardTypeAxis_2ce3e800-d5db-4ef2-8ebc-db04c450b614" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_2ce3e800-d5db-4ef2-8ebc-db04c450b614_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_AwardTypeAxis_2ce3e800-d5db-4ef2-8ebc-db04c450b614" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_2ce3e800-d5db-4ef2-8ebc-db04c450b614_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_d46046d9-6744-467a-afaa-e0ad44d01a83" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_AwardTypeAxis_2ce3e800-d5db-4ef2-8ebc-db04c450b614" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_d46046d9-6744-467a-afaa-e0ad44d01a83" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_ValueAppreciationPoolMember_d2750e6e-874d-4548-9cb6-e9e5156caffb" xlink:href="hg-20240930.xsd#hg_ValueAppreciationPoolMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_d46046d9-6744-467a-afaa-e0ad44d01a83" xlink:to="loc_hg_ValueAppreciationPoolMember_d2750e6e-874d-4548-9cb6-e9e5156caffb" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_ShareBasedPaymentArrangementPercentOfIncreaseInFairMarketValueAwardedToEmployees_c1990cb5-1afd-40d7-9660-05b0d3575347" xlink:href="hg-20240930.xsd#hg_ShareBasedPaymentArrangementPercentOfIncreaseInFairMarketValueAwardedToEmployees"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems_1f896058-052c-46e6-98a3-318074affd10" xlink:to="loc_hg_ShareBasedPaymentArrangementPercentOfIncreaseInFairMarketValueAwardedToEmployees_c1990cb5-1afd-40d7-9660-05b0d3575347" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage_7150afd7-50c0-4f01-a7dc-94effe9111b7" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems_1f896058-052c-46e6-98a3-318074affd10" xlink:to="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage_7150afd7-50c0-4f01-a7dc-94effe9111b7" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllocatedShareBasedCompensationExpense_87f727ce-f7bf-4196-8692-8d5c72fc2fae" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AllocatedShareBasedCompensationExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems_1f896058-052c-46e6-98a3-318074affd10" xlink:to="loc_us-gaap_AllocatedShareBasedCompensationExpense_87f727ce-f7bf-4196-8692-8d5c72fc2fae" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_8c5b68b6-ae02-4001-ba37-97de91a5f4b8" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems_1f896058-052c-46e6-98a3-318074affd10" xlink:to="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_8c5b68b6-ae02-4001-ba37-97de91a5f4b8" xlink:type="arc" order="3"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/ReinsuranceNarrativeDetails" xlink:type="simple" xlink:href="hg-20240930.xsd#ReinsuranceNarrativeDetails"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/ReinsuranceNarrativeDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskLineItems_48a95b80-cda1-4eaf-bab5-3b8222cb325f" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CededCreditRiskLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskTable_974d3ad2-d383-4540-a870-d5f252af5464" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CededCreditRiskTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_CededCreditRiskLineItems_48a95b80-cda1-4eaf-bab5-3b8222cb325f" xlink:to="loc_us-gaap_CededCreditRiskTable_974d3ad2-d383-4540-a870-d5f252af5464" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskAxis_0f2931f6-04ce-401d-a412-481e9e09de98" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CededCreditRiskAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_CededCreditRiskTable_974d3ad2-d383-4540-a870-d5f252af5464" xlink:to="loc_us-gaap_CededCreditRiskAxis_0f2931f6-04ce-401d-a412-481e9e09de98" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskReinsurerDomain_0f2931f6-04ce-401d-a412-481e9e09de98_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CededCreditRiskReinsurerDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_CededCreditRiskAxis_0f2931f6-04ce-401d-a412-481e9e09de98" xlink:to="loc_us-gaap_CededCreditRiskReinsurerDomain_0f2931f6-04ce-401d-a412-481e9e09de98_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskReinsurerDomain_15d7d9c1-6f86-4c90-873b-91732d905c08" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CededCreditRiskReinsurerDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_CededCreditRiskAxis_0f2931f6-04ce-401d-a412-481e9e09de98" xlink:to="loc_us-gaap_CededCreditRiskReinsurerDomain_15d7d9c1-6f86-4c90-873b-91732d905c08" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_ReinsurerOneMember_843fa2ab-c287-45d4-9918-0e80bb94a796" xlink:href="hg-20240930.xsd#hg_ReinsurerOneMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CededCreditRiskReinsurerDomain_15d7d9c1-6f86-4c90-873b-91732d905c08" xlink:to="loc_hg_ReinsurerOneMember_843fa2ab-c287-45d4-9918-0e80bb94a796" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_ReinsurerTwoMember_b894293d-0aac-43ed-be6c-29345d33a854" xlink:href="hg-20240930.xsd#hg_ReinsurerTwoMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CededCreditRiskReinsurerDomain_15d7d9c1-6f86-4c90-873b-91732d905c08" xlink:to="loc_hg_ReinsurerTwoMember_b894293d-0aac-43ed-be6c-29345d33a854" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_ReinsurerThreeMember_651eca86-0b8a-4bbc-976a-021028b6ad09" xlink:href="hg-20240930.xsd#hg_ReinsurerThreeMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CededCreditRiskReinsurerDomain_15d7d9c1-6f86-4c90-873b-91732d905c08" xlink:to="loc_hg_ReinsurerThreeMember_651eca86-0b8a-4bbc-976a-021028b6ad09" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByBenchmarkAxis_764fbad7-0c0a-42c1-abfb-4897b2a88fd2" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskByBenchmarkAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_CededCreditRiskTable_974d3ad2-d383-4540-a870-d5f252af5464" xlink:to="loc_us-gaap_ConcentrationRiskByBenchmarkAxis_764fbad7-0c0a-42c1-abfb-4897b2a88fd2" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskBenchmarkDomain_764fbad7-0c0a-42c1-abfb-4897b2a88fd2_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskBenchmarkDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_ConcentrationRiskByBenchmarkAxis_764fbad7-0c0a-42c1-abfb-4897b2a88fd2" xlink:to="loc_us-gaap_ConcentrationRiskBenchmarkDomain_764fbad7-0c0a-42c1-abfb-4897b2a88fd2_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskBenchmarkDomain_66bd06ae-f816-489a-ad5b-3a784067be41" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskBenchmarkDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_ConcentrationRiskByBenchmarkAxis_764fbad7-0c0a-42c1-abfb-4897b2a88fd2" xlink:to="loc_us-gaap_ConcentrationRiskBenchmarkDomain_66bd06ae-f816-489a-ad5b-3a784067be41" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsMember_b410e811-5a0e-413c-8a6d-0c6c0cdeef48" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ConcentrationRiskBenchmarkDomain_66bd06ae-f816-489a-ad5b-3a784067be41" xlink:to="loc_us-gaap_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsMember_b410e811-5a0e-413c-8a6d-0c6c0cdeef48" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByTypeAxis_ee0de17e-c8dd-4bb0-8d77-6c6d37e2c826" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskByTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_CededCreditRiskTable_974d3ad2-d383-4540-a870-d5f252af5464" xlink:to="loc_us-gaap_ConcentrationRiskByTypeAxis_ee0de17e-c8dd-4bb0-8d77-6c6d37e2c826" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskTypeDomain_ee0de17e-c8dd-4bb0-8d77-6c6d37e2c826_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_ConcentrationRiskByTypeAxis_ee0de17e-c8dd-4bb0-8d77-6c6d37e2c826" xlink:to="loc_us-gaap_ConcentrationRiskTypeDomain_ee0de17e-c8dd-4bb0-8d77-6c6d37e2c826_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskTypeDomain_f8463ae4-2b8b-4bdf-8cbc-fc38d6597751" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_ConcentrationRiskByTypeAxis_ee0de17e-c8dd-4bb0-8d77-6c6d37e2c826" xlink:to="loc_us-gaap_ConcentrationRiskTypeDomain_f8463ae4-2b8b-4bdf-8cbc-fc38d6597751" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsurerConcentrationRiskMember_aabe61c3-c7d9-4c29-84d8-52e8ea00a8f4" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ReinsurerConcentrationRiskMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ConcentrationRiskTypeDomain_f8463ae4-2b8b-4bdf-8cbc-fc38d6597751" xlink:to="loc_us-gaap_ReinsurerConcentrationRiskMember_aabe61c3-c7d9-4c29-84d8-52e8ea00a8f4" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceContractAxis_cff033b4-801b-4881-87e2-41d87d2679d5" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ReinsuranceContractAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_CededCreditRiskTable_974d3ad2-d383-4540-a870-d5f252af5464" xlink:to="loc_us-gaap_ReinsuranceContractAxis_cff033b4-801b-4881-87e2-41d87d2679d5" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_f655dfd8-969a-4317-9257-8ebff5eafc98" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_CededCreditRiskTable_974d3ad2-d383-4540-a870-d5f252af5464" xlink:to="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_f655dfd8-969a-4317-9257-8ebff5eafc98" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDomain_f655dfd8-969a-4317-9257-8ebff5eafc98_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RelatedPartyDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_f655dfd8-969a-4317-9257-8ebff5eafc98" xlink:to="loc_us-gaap_RelatedPartyDomain_f655dfd8-969a-4317-9257-8ebff5eafc98_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDomain_3111e9db-a91d-464d-8779-22dda125eeed" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RelatedPartyDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_f655dfd8-969a-4317-9257-8ebff5eafc98" xlink:to="loc_us-gaap_RelatedPartyDomain_3111e9db-a91d-464d-8779-22dda125eeed" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyMember_608f339b-ff1d-42a5-817a-578cbd08ed96" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RelatedPartyMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyDomain_3111e9db-a91d-464d-8779-22dda125eeed" xlink:to="loc_us-gaap_RelatedPartyMember_608f339b-ff1d-42a5-817a-578cbd08ed96" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts_fbcd306b-54d7-40ca-a73c-aa2c4b20afdc" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CededCreditRiskLineItems_48a95b80-cda1-4eaf-bab5-3b8222cb325f" xlink:to="loc_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts_fbcd306b-54d7-40ca-a73c-aa2c4b20afdc" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsReceivableAtCarryingValue_8c4a6fcf-0655-4cb4-8b7f-e157737a3bb6" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PremiumsReceivableAtCarryingValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CededCreditRiskLineItems_48a95b80-cda1-4eaf-bab5-3b8222cb325f" xlink:to="loc_us-gaap_PremiumsReceivableAtCarryingValue_8c4a6fcf-0655-4cb4-8b7f-e157737a3bb6" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverablesOnPaidLosses_9a892e0f-4f31-4270-a6b4-d10050764cff" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ReinsuranceRecoverablesOnPaidLosses"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CededCreditRiskLineItems_48a95b80-cda1-4eaf-bab5-3b8222cb325f" xlink:to="loc_us-gaap_ReinsuranceRecoverablesOnPaidLosses_9a892e0f-4f31-4270-a6b4-d10050764cff" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments_0888ce72-bf4c-488e-ab1d-462250b2b78e" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CededCreditRiskLineItems_48a95b80-cda1-4eaf-bab5-3b8222cb325f" xlink:to="loc_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments_0888ce72-bf4c-488e-ab1d-462250b2b78e" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverablesAllowance_7b321a10-59ea-4212-b3cf-b1a74af7a18b" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ReinsuranceRecoverablesAllowance"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CededCreditRiskLineItems_48a95b80-cda1-4eaf-bab5-3b8222cb325f" xlink:to="loc_us-gaap_ReinsuranceRecoverablesAllowance_7b321a10-59ea-4212-b3cf-b1a74af7a18b" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskPercentage1_f2c7d497-80c2-4393-812b-794baeab982c" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskPercentage1"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CededCreditRiskLineItems_48a95b80-cda1-4eaf-bab5-3b8222cb325f" xlink:to="loc_us-gaap_ConcentrationRiskPercentage1_f2c7d497-80c2-4393-812b-794baeab982c" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededPremiumsWritten_c5aad1ea-c17c-46f5-87ba-add042b6a3d9" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CededPremiumsWritten"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CededCreditRiskLineItems_48a95b80-cda1-4eaf-bab5-3b8222cb325f" xlink:to="loc_us-gaap_CededPremiumsWritten_c5aad1ea-c17c-46f5-87ba-add042b6a3d9" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_LiabilityForClaimsAndClaimsAdjustmentExpenseAmortizationOfDeferredGain_37e29f4c-03d0-4d8a-b43f-e8bfa804255d" xlink:href="hg-20240930.xsd#hg_LiabilityForClaimsAndClaimsAdjustmentExpenseAmortizationOfDeferredGain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CededCreditRiskLineItems_48a95b80-cda1-4eaf-bab5-3b8222cb325f" xlink:to="loc_hg_LiabilityForClaimsAndClaimsAdjustmentExpenseAmortizationOfDeferredGain_37e29f4c-03d0-4d8a-b43f-e8bfa804255d" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_RelatedPartyTransactionRiskTransferCapacity_7ca0b273-c830-4026-8837-624965a99b1e" xlink:href="hg-20240930.xsd#hg_RelatedPartyTransactionRiskTransferCapacity"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CededCreditRiskLineItems_48a95b80-cda1-4eaf-bab5-3b8222cb325f" xlink:to="loc_hg_RelatedPartyTransactionRiskTransferCapacity_7ca0b273-c830-4026-8837-624965a99b1e" xlink:type="arc" order="8"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/ReinsuranceNarrativeDetails_1" xlink:type="simple" xlink:href="hg-20240930.xsd#ReinsuranceNarrativeDetails_1"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/ReinsuranceNarrativeDetails_1" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskLineItems_48a95b80-cda1-4eaf-bab5-3b8222cb325f" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CededCreditRiskLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskTable_974d3ad2-d383-4540-a870-d5f252af5464" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CededCreditRiskTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_CededCreditRiskLineItems_48a95b80-cda1-4eaf-bab5-3b8222cb325f" xlink:to="loc_us-gaap_CededCreditRiskTable_974d3ad2-d383-4540-a870-d5f252af5464" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskAxis_0f2931f6-04ce-401d-a412-481e9e09de98" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CededCreditRiskAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_CededCreditRiskTable_974d3ad2-d383-4540-a870-d5f252af5464" xlink:to="loc_us-gaap_CededCreditRiskAxis_0f2931f6-04ce-401d-a412-481e9e09de98" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskReinsurerDomain_0f2931f6-04ce-401d-a412-481e9e09de98_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CededCreditRiskReinsurerDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_CededCreditRiskAxis_0f2931f6-04ce-401d-a412-481e9e09de98" xlink:to="loc_us-gaap_CededCreditRiskReinsurerDomain_0f2931f6-04ce-401d-a412-481e9e09de98_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskReinsurerDomain_15d7d9c1-6f86-4c90-873b-91732d905c08" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CededCreditRiskReinsurerDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_CededCreditRiskAxis_0f2931f6-04ce-401d-a412-481e9e09de98" xlink:to="loc_us-gaap_CededCreditRiskReinsurerDomain_15d7d9c1-6f86-4c90-873b-91732d905c08" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_ReinsurerOneMember_843fa2ab-c287-45d4-9918-0e80bb94a796" xlink:href="hg-20240930.xsd#hg_ReinsurerOneMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CededCreditRiskReinsurerDomain_15d7d9c1-6f86-4c90-873b-91732d905c08" xlink:to="loc_hg_ReinsurerOneMember_843fa2ab-c287-45d4-9918-0e80bb94a796" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_ReinsurerTwoMember_b894293d-0aac-43ed-be6c-29345d33a854" xlink:href="hg-20240930.xsd#hg_ReinsurerTwoMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CededCreditRiskReinsurerDomain_15d7d9c1-6f86-4c90-873b-91732d905c08" xlink:to="loc_hg_ReinsurerTwoMember_b894293d-0aac-43ed-be6c-29345d33a854" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_ReinsurerThreeMember_651eca86-0b8a-4bbc-976a-021028b6ad09" xlink:href="hg-20240930.xsd#hg_ReinsurerThreeMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CededCreditRiskReinsurerDomain_15d7d9c1-6f86-4c90-873b-91732d905c08" xlink:to="loc_hg_ReinsurerThreeMember_651eca86-0b8a-4bbc-976a-021028b6ad09" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByBenchmarkAxis_764fbad7-0c0a-42c1-abfb-4897b2a88fd2" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskByBenchmarkAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_CededCreditRiskTable_974d3ad2-d383-4540-a870-d5f252af5464" xlink:to="loc_us-gaap_ConcentrationRiskByBenchmarkAxis_764fbad7-0c0a-42c1-abfb-4897b2a88fd2" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskBenchmarkDomain_764fbad7-0c0a-42c1-abfb-4897b2a88fd2_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskBenchmarkDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_ConcentrationRiskByBenchmarkAxis_764fbad7-0c0a-42c1-abfb-4897b2a88fd2" xlink:to="loc_us-gaap_ConcentrationRiskBenchmarkDomain_764fbad7-0c0a-42c1-abfb-4897b2a88fd2_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskBenchmarkDomain_66bd06ae-f816-489a-ad5b-3a784067be41" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskBenchmarkDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_ConcentrationRiskByBenchmarkAxis_764fbad7-0c0a-42c1-abfb-4897b2a88fd2" xlink:to="loc_us-gaap_ConcentrationRiskBenchmarkDomain_66bd06ae-f816-489a-ad5b-3a784067be41" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsMember_b410e811-5a0e-413c-8a6d-0c6c0cdeef48" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ConcentrationRiskBenchmarkDomain_66bd06ae-f816-489a-ad5b-3a784067be41" xlink:to="loc_us-gaap_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsMember_b410e811-5a0e-413c-8a6d-0c6c0cdeef48" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByTypeAxis_ee0de17e-c8dd-4bb0-8d77-6c6d37e2c826" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskByTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_CededCreditRiskTable_974d3ad2-d383-4540-a870-d5f252af5464" xlink:to="loc_us-gaap_ConcentrationRiskByTypeAxis_ee0de17e-c8dd-4bb0-8d77-6c6d37e2c826" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskTypeDomain_ee0de17e-c8dd-4bb0-8d77-6c6d37e2c826_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_ConcentrationRiskByTypeAxis_ee0de17e-c8dd-4bb0-8d77-6c6d37e2c826" xlink:to="loc_us-gaap_ConcentrationRiskTypeDomain_ee0de17e-c8dd-4bb0-8d77-6c6d37e2c826_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskTypeDomain_f8463ae4-2b8b-4bdf-8cbc-fc38d6597751" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_ConcentrationRiskByTypeAxis_ee0de17e-c8dd-4bb0-8d77-6c6d37e2c826" xlink:to="loc_us-gaap_ConcentrationRiskTypeDomain_f8463ae4-2b8b-4bdf-8cbc-fc38d6597751" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsurerConcentrationRiskMember_aabe61c3-c7d9-4c29-84d8-52e8ea00a8f4" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ReinsurerConcentrationRiskMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ConcentrationRiskTypeDomain_f8463ae4-2b8b-4bdf-8cbc-fc38d6597751" xlink:to="loc_us-gaap_ReinsurerConcentrationRiskMember_aabe61c3-c7d9-4c29-84d8-52e8ea00a8f4" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_f655dfd8-969a-4317-9257-8ebff5eafc98" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_CededCreditRiskTable_974d3ad2-d383-4540-a870-d5f252af5464" xlink:to="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_f655dfd8-969a-4317-9257-8ebff5eafc98" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDomain_f655dfd8-969a-4317-9257-8ebff5eafc98_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RelatedPartyDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_f655dfd8-969a-4317-9257-8ebff5eafc98" xlink:to="loc_us-gaap_RelatedPartyDomain_f655dfd8-969a-4317-9257-8ebff5eafc98_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDomain_3111e9db-a91d-464d-8779-22dda125eeed" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RelatedPartyDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_f655dfd8-969a-4317-9257-8ebff5eafc98" xlink:to="loc_us-gaap_RelatedPartyDomain_3111e9db-a91d-464d-8779-22dda125eeed" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyMember_608f339b-ff1d-42a5-817a-578cbd08ed96" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RelatedPartyMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyDomain_3111e9db-a91d-464d-8779-22dda125eeed" xlink:to="loc_us-gaap_RelatedPartyMember_608f339b-ff1d-42a5-817a-578cbd08ed96" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts_fbcd306b-54d7-40ca-a73c-aa2c4b20afdc" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CededCreditRiskLineItems_48a95b80-cda1-4eaf-bab5-3b8222cb325f" xlink:to="loc_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts_fbcd306b-54d7-40ca-a73c-aa2c4b20afdc" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsReceivableAtCarryingValue_8c4a6fcf-0655-4cb4-8b7f-e157737a3bb6" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PremiumsReceivableAtCarryingValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CededCreditRiskLineItems_48a95b80-cda1-4eaf-bab5-3b8222cb325f" xlink:to="loc_us-gaap_PremiumsReceivableAtCarryingValue_8c4a6fcf-0655-4cb4-8b7f-e157737a3bb6" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverablesOnPaidLosses_9a892e0f-4f31-4270-a6b4-d10050764cff" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ReinsuranceRecoverablesOnPaidLosses"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CededCreditRiskLineItems_48a95b80-cda1-4eaf-bab5-3b8222cb325f" xlink:to="loc_us-gaap_ReinsuranceRecoverablesOnPaidLosses_9a892e0f-4f31-4270-a6b4-d10050764cff" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments_0888ce72-bf4c-488e-ab1d-462250b2b78e" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CededCreditRiskLineItems_48a95b80-cda1-4eaf-bab5-3b8222cb325f" xlink:to="loc_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments_0888ce72-bf4c-488e-ab1d-462250b2b78e" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverablesAllowance_7b321a10-59ea-4212-b3cf-b1a74af7a18b" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ReinsuranceRecoverablesAllowance"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CededCreditRiskLineItems_48a95b80-cda1-4eaf-bab5-3b8222cb325f" xlink:to="loc_us-gaap_ReinsuranceRecoverablesAllowance_7b321a10-59ea-4212-b3cf-b1a74af7a18b" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskPercentage1_f2c7d497-80c2-4393-812b-794baeab982c" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskPercentage1"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CededCreditRiskLineItems_48a95b80-cda1-4eaf-bab5-3b8222cb325f" xlink:to="loc_us-gaap_ConcentrationRiskPercentage1_f2c7d497-80c2-4393-812b-794baeab982c" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededPremiumsWritten_c5aad1ea-c17c-46f5-87ba-add042b6a3d9" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CededPremiumsWritten"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CededCreditRiskLineItems_48a95b80-cda1-4eaf-bab5-3b8222cb325f" xlink:to="loc_us-gaap_CededPremiumsWritten_c5aad1ea-c17c-46f5-87ba-add042b6a3d9" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_LiabilityForClaimsAndClaimsAdjustmentExpenseAmortizationOfDeferredGain_37e29f4c-03d0-4d8a-b43f-e8bfa804255d" xlink:href="hg-20240930.xsd#hg_LiabilityForClaimsAndClaimsAdjustmentExpenseAmortizationOfDeferredGain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CededCreditRiskLineItems_48a95b80-cda1-4eaf-bab5-3b8222cb325f" xlink:to="loc_hg_LiabilityForClaimsAndClaimsAdjustmentExpenseAmortizationOfDeferredGain_37e29f4c-03d0-4d8a-b43f-e8bfa804255d" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_RelatedPartyTransactionRiskTransferCapacity_7ca0b273-c830-4026-8837-624965a99b1e" xlink:href="hg-20240930.xsd#hg_RelatedPartyTransactionRiskTransferCapacity"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CededCreditRiskLineItems_48a95b80-cda1-4eaf-bab5-3b8222cb325f" xlink:to="loc_hg_RelatedPartyTransactionRiskTransferCapacity_7ca0b273-c830-4026-8837-624965a99b1e" xlink:type="arc" order="8"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/ReinsuranceScheduleofPaidandUnpaidLossesandLossAdjustmentExpensesRecoverableDetails" xlink:type="simple" xlink:href="hg-20240930.xsd#ReinsuranceScheduleofPaidandUnpaidLossesandLossAdjustmentExpensesRecoverableDetails"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/ReinsuranceScheduleofPaidandUnpaidLossesandLossAdjustmentExpensesRecoverableDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskLineItems_af966522-8981-457e-ae55-b5535868c2e6" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CededCreditRiskLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskTable_000405cd-aa2e-46bb-af35-3bae535c735f" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CededCreditRiskTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_CededCreditRiskLineItems_af966522-8981-457e-ae55-b5535868c2e6" xlink:to="loc_us-gaap_CededCreditRiskTable_000405cd-aa2e-46bb-af35-3bae535c735f" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskCollateralizationAxis_72f3a25a-082f-4ccc-8131-a3eacdac9ad9" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CededCreditRiskCollateralizationAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_CededCreditRiskTable_000405cd-aa2e-46bb-af35-3bae535c735f" xlink:to="loc_us-gaap_CededCreditRiskCollateralizationAxis_72f3a25a-082f-4ccc-8131-a3eacdac9ad9" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskCollateralizationDomain_72f3a25a-082f-4ccc-8131-a3eacdac9ad9_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CededCreditRiskCollateralizationDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_CededCreditRiskCollateralizationAxis_72f3a25a-082f-4ccc-8131-a3eacdac9ad9" xlink:to="loc_us-gaap_CededCreditRiskCollateralizationDomain_72f3a25a-082f-4ccc-8131-a3eacdac9ad9_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskCollateralizationDomain_1ab58540-5453-4941-8984-7998d169d9b8" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CededCreditRiskCollateralizationDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_CededCreditRiskCollateralizationAxis_72f3a25a-082f-4ccc-8131-a3eacdac9ad9" xlink:to="loc_us-gaap_CededCreditRiskCollateralizationDomain_1ab58540-5453-4941-8984-7998d169d9b8" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskSecuredMember_9a935057-7f49-46f3-9ec3-5478a83528b5" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CededCreditRiskSecuredMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CededCreditRiskCollateralizationDomain_1ab58540-5453-4941-8984-7998d169d9b8" xlink:to="loc_us-gaap_CededCreditRiskSecuredMember_9a935057-7f49-46f3-9ec3-5478a83528b5" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByBenchmarkAxis_b3c63baa-07e1-4057-8df5-2bfa3c8c0651" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskByBenchmarkAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_CededCreditRiskTable_000405cd-aa2e-46bb-af35-3bae535c735f" xlink:to="loc_us-gaap_ConcentrationRiskByBenchmarkAxis_b3c63baa-07e1-4057-8df5-2bfa3c8c0651" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskBenchmarkDomain_b3c63baa-07e1-4057-8df5-2bfa3c8c0651_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskBenchmarkDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_ConcentrationRiskByBenchmarkAxis_b3c63baa-07e1-4057-8df5-2bfa3c8c0651" xlink:to="loc_us-gaap_ConcentrationRiskBenchmarkDomain_b3c63baa-07e1-4057-8df5-2bfa3c8c0651_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskBenchmarkDomain_496d5107-8fa0-418c-893e-0b7f702fa78b" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskBenchmarkDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_ConcentrationRiskByBenchmarkAxis_b3c63baa-07e1-4057-8df5-2bfa3c8c0651" xlink:to="loc_us-gaap_ConcentrationRiskBenchmarkDomain_496d5107-8fa0-418c-893e-0b7f702fa78b" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsMember_6a3ca6ca-7c1f-42b0-afe4-cf5cfbc2ff17" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ConcentrationRiskBenchmarkDomain_496d5107-8fa0-418c-893e-0b7f702fa78b" xlink:to="loc_us-gaap_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsMember_6a3ca6ca-7c1f-42b0-afe4-cf5cfbc2ff17" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByTypeAxis_e22d1e7a-9c08-4903-84d5-ff5fbf792e60" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskByTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_CededCreditRiskTable_000405cd-aa2e-46bb-af35-3bae535c735f" xlink:to="loc_us-gaap_ConcentrationRiskByTypeAxis_e22d1e7a-9c08-4903-84d5-ff5fbf792e60" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskTypeDomain_e22d1e7a-9c08-4903-84d5-ff5fbf792e60_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_ConcentrationRiskByTypeAxis_e22d1e7a-9c08-4903-84d5-ff5fbf792e60" xlink:to="loc_us-gaap_ConcentrationRiskTypeDomain_e22d1e7a-9c08-4903-84d5-ff5fbf792e60_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskTypeDomain_514bf7b0-fb36-47f9-80b2-aa1f2b76d15f" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_ConcentrationRiskByTypeAxis_e22d1e7a-9c08-4903-84d5-ff5fbf792e60" xlink:to="loc_us-gaap_ConcentrationRiskTypeDomain_514bf7b0-fb36-47f9-80b2-aa1f2b76d15f" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsurerConcentrationRiskMember_0d0be210-d073-43e1-bb7f-147acdd2e7c7" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ReinsurerConcentrationRiskMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ConcentrationRiskTypeDomain_514bf7b0-fb36-47f9-80b2-aa1f2b76d15f" xlink:to="loc_us-gaap_ReinsurerConcentrationRiskMember_0d0be210-d073-43e1-bb7f-147acdd2e7c7" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_CreditRatingMajorRatingAgenciesAxis_2473cc57-d0c0-4c2e-aa36-2754e093ee49" xlink:href="hg-20240930.xsd#hg_CreditRatingMajorRatingAgenciesAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_CededCreditRiskTable_000405cd-aa2e-46bb-af35-3bae535c735f" xlink:to="loc_hg_CreditRatingMajorRatingAgenciesAxis_2473cc57-d0c0-4c2e-aa36-2754e093ee49" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_CreditRatingMajorRatingAgenciesDomain_2473cc57-d0c0-4c2e-aa36-2754e093ee49_default" xlink:href="hg-20240930.xsd#hg_CreditRatingMajorRatingAgenciesDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_hg_CreditRatingMajorRatingAgenciesAxis_2473cc57-d0c0-4c2e-aa36-2754e093ee49" xlink:to="loc_hg_CreditRatingMajorRatingAgenciesDomain_2473cc57-d0c0-4c2e-aa36-2754e093ee49_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_CreditRatingMajorRatingAgenciesDomain_fc093458-f814-498d-ab39-c9f7b2936061" xlink:href="hg-20240930.xsd#hg_CreditRatingMajorRatingAgenciesDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_hg_CreditRatingMajorRatingAgenciesAxis_2473cc57-d0c0-4c2e-aa36-2754e093ee49" xlink:to="loc_hg_CreditRatingMajorRatingAgenciesDomain_fc093458-f814-498d-ab39-c9f7b2936061" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_AOrBetterRatingMember_fd667ebf-95cb-4fd7-bb97-a974083624ee" xlink:href="hg-20240930.xsd#hg_AOrBetterRatingMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_hg_CreditRatingMajorRatingAgenciesDomain_fc093458-f814-498d-ab39-c9f7b2936061" xlink:to="loc_hg_AOrBetterRatingMember_fd667ebf-95cb-4fd7-bb97-a974083624ee" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_BelowARatingMember_783f75a0-56df-47b1-82c6-17c13590bb10" xlink:href="hg-20240930.xsd#hg_BelowARatingMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_hg_CreditRatingMajorRatingAgenciesDomain_fc093458-f814-498d-ab39-c9f7b2936061" xlink:to="loc_hg_BelowARatingMember_783f75a0-56df-47b1-82c6-17c13590bb10" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskPercentage1_f28a1fe2-eee9-4cfc-9ad4-1215349e5ce8" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskPercentage1"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CededCreditRiskLineItems_af966522-8981-457e-ae55-b5535868c2e6" xlink:to="loc_us-gaap_ConcentrationRiskPercentage1_f28a1fe2-eee9-4cfc-9ad4-1215349e5ce8" xlink:type="arc" order="0"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/ReserveforLossesandLossAdjustmentExpensesNarrativeDetails" xlink:type="simple" xlink:href="hg-20240930.xsd#ReserveforLossesandLossAdjustmentExpensesNarrativeDetails"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/ReserveforLossesandLossAdjustmentExpensesNarrativeDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseLineItems_74ba2ad9-fe7b-45a4-806f-f4090299ea99" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseTable_6806cf03-8542-421a-b501-843be86cf7ce" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseLineItems_74ba2ad9-fe7b-45a4-806f-f4090299ea99" xlink:to="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseTable_6806cf03-8542-421a-b501-843be86cf7ce" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForCatastropheClaimsByCatastrophicEventAxis_565d2d18-791d-434a-879f-8598f875ec97" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LiabilityForCatastropheClaimsByCatastrophicEventAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseTable_6806cf03-8542-421a-b501-843be86cf7ce" xlink:to="loc_us-gaap_LiabilityForCatastropheClaimsByCatastrophicEventAxis_565d2d18-791d-434a-879f-8598f875ec97" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CatastrophicEventDomain_565d2d18-791d-434a-879f-8598f875ec97_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CatastrophicEventDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_LiabilityForCatastropheClaimsByCatastrophicEventAxis_565d2d18-791d-434a-879f-8598f875ec97" xlink:to="loc_us-gaap_CatastrophicEventDomain_565d2d18-791d-434a-879f-8598f875ec97_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CatastrophicEventDomain_5f66afed-2817-4947-a1f2-83005a38b149" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CatastrophicEventDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_LiabilityForCatastropheClaimsByCatastrophicEventAxis_565d2d18-791d-434a-879f-8598f875ec97" xlink:to="loc_us-gaap_CatastrophicEventDomain_5f66afed-2817-4947-a1f2-83005a38b149" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_CatastropheLossesMember_abea67ee-0b97-47be-8464-6f47cbb2edcf" xlink:href="hg-20240930.xsd#hg_CatastropheLossesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CatastrophicEventDomain_5f66afed-2817-4947-a1f2-83005a38b149" xlink:to="loc_hg_CatastropheLossesMember_abea67ee-0b97-47be-8464-6f47cbb2edcf" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncatastrophicEventAxis_0fcd3377-e2fb-4172-ad72-04c39c469abf" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NoncatastrophicEventAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseTable_6806cf03-8542-421a-b501-843be86cf7ce" xlink:to="loc_us-gaap_NoncatastrophicEventAxis_0fcd3377-e2fb-4172-ad72-04c39c469abf" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncatastrophicEventDomain_0fcd3377-e2fb-4172-ad72-04c39c469abf_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NoncatastrophicEventDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_NoncatastrophicEventAxis_0fcd3377-e2fb-4172-ad72-04c39c469abf" xlink:to="loc_us-gaap_NoncatastrophicEventDomain_0fcd3377-e2fb-4172-ad72-04c39c469abf_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncatastrophicEventDomain_fad53cec-9e77-419f-875c-eb3ce3518c34" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NoncatastrophicEventDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_NoncatastrophicEventAxis_0fcd3377-e2fb-4172-ad72-04c39c469abf" xlink:to="loc_us-gaap_NoncatastrophicEventDomain_fad53cec-9e77-419f-875c-eb3ce3518c34" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_AttritionalLossesMember_a732f51f-5c18-4692-95e6-090ed69ecd75" xlink:href="hg-20240930.xsd#hg_AttritionalLossesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_NoncatastrophicEventDomain_fad53cec-9e77-419f-875c-eb3ce3518c34" xlink:to="loc_hg_AttritionalLossesMember_a732f51f-5c18-4692-95e6-090ed69ecd75" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductOrServiceAxis_49dc80b4-53cc-4e73-a66d-21876123188f" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ProductOrServiceAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseTable_6806cf03-8542-421a-b501-843be86cf7ce" xlink:to="loc_srt_ProductOrServiceAxis_49dc80b4-53cc-4e73-a66d-21876123188f" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductsAndServicesDomain_49dc80b4-53cc-4e73-a66d-21876123188f_default" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ProductsAndServicesDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_ProductOrServiceAxis_49dc80b4-53cc-4e73-a66d-21876123188f" xlink:to="loc_srt_ProductsAndServicesDomain_49dc80b4-53cc-4e73-a66d-21876123188f_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductsAndServicesDomain_6ee89557-cb2d-4bfc-989f-0cdccac8fbd5" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ProductsAndServicesDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_ProductOrServiceAxis_49dc80b4-53cc-4e73-a66d-21876123188f" xlink:to="loc_srt_ProductsAndServicesDomain_6ee89557-cb2d-4bfc-989f-0cdccac8fbd5" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_SpecialtyContractsMember_9dc11119-ad2c-4b36-b4b9-fa5525ce5d5c" xlink:href="hg-20240930.xsd#hg_SpecialtyContractsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ProductsAndServicesDomain_6ee89557-cb2d-4bfc-989f-0cdccac8fbd5" xlink:to="loc_hg_SpecialtyContractsMember_9dc11119-ad2c-4b36-b4b9-fa5525ce5d5c" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_CasualtyLinesMember_d0159ad1-8e5c-4634-bcce-1896f17a566e" xlink:href="hg-20240930.xsd#hg_CasualtyLinesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ProductsAndServicesDomain_6ee89557-cb2d-4bfc-989f-0cdccac8fbd5" xlink:to="loc_hg_CasualtyLinesMember_d0159ad1-8e5c-4634-bcce-1896f17a566e" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_PropertyContractsMember_6d1d3a7a-d8a6-4d12-a28b-5b96f4eb3323" xlink:href="hg-20240930.xsd#hg_PropertyContractsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ProductsAndServicesDomain_6ee89557-cb2d-4bfc-989f-0cdccac8fbd5" xlink:to="loc_hg_PropertyContractsMember_6d1d3a7a-d8a6-4d12-a28b-5b96f4eb3323" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_CasualtyLinesOfBusinessMember_d0ae47f7-a5a4-4b2a-9513-644aa9e11a3a" xlink:href="hg-20240930.xsd#hg_CasualtyLinesOfBusinessMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ProductsAndServicesDomain_6ee89557-cb2d-4bfc-989f-0cdccac8fbd5" xlink:to="loc_hg_CasualtyLinesOfBusinessMember_d0ae47f7-a5a4-4b2a-9513-644aa9e11a3a" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnusualOrInfrequentItemAxis_b13bce9f-8cc2-4ba1-ba88-3bdfe49871c9" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_UnusualOrInfrequentItemAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseTable_6806cf03-8542-421a-b501-843be86cf7ce" xlink:to="loc_us-gaap_UnusualOrInfrequentItemAxis_b13bce9f-8cc2-4ba1-ba88-3bdfe49871c9" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnusualOrInfrequentItemDomain_b13bce9f-8cc2-4ba1-ba88-3bdfe49871c9_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_UnusualOrInfrequentItemDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_UnusualOrInfrequentItemAxis_b13bce9f-8cc2-4ba1-ba88-3bdfe49871c9" xlink:to="loc_us-gaap_UnusualOrInfrequentItemDomain_b13bce9f-8cc2-4ba1-ba88-3bdfe49871c9_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnusualOrInfrequentItemDomain_f31df4db-9968-44c6-a638-095f04554745" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_UnusualOrInfrequentItemDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_UnusualOrInfrequentItemAxis_b13bce9f-8cc2-4ba1-ba88-3bdfe49871c9" xlink:to="loc_us-gaap_UnusualOrInfrequentItemDomain_f31df4db-9968-44c6-a638-095f04554745" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_HurricaneHeleneMember_70617502-5fbb-4e31-9285-7ac7bd433e25" xlink:href="hg-20240930.xsd#hg_HurricaneHeleneMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_UnusualOrInfrequentItemDomain_f31df4db-9968-44c6-a638-095f04554745" xlink:to="loc_hg_HurricaneHeleneMember_70617502-5fbb-4e31-9285-7ac7bd433e25" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_BaltimoreBridgeMember_0c2822d3-8e0e-4bbd-a9e3-6bbb7826103c" xlink:href="hg-20240930.xsd#hg_BaltimoreBridgeMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_UnusualOrInfrequentItemDomain_f31df4db-9968-44c6-a638-095f04554745" xlink:to="loc_hg_BaltimoreBridgeMember_0c2822d3-8e0e-4bbd-a9e3-6bbb7826103c" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_UkrainianConflictMember_96c98372-27b4-4b9c-bc9b-8d6c9ccb83c9" xlink:href="hg-20240930.xsd#hg_UkrainianConflictMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_UnusualOrInfrequentItemDomain_f31df4db-9968-44c6-a638-095f04554745" xlink:to="loc_hg_UkrainianConflictMember_96c98372-27b4-4b9c-bc9b-8d6c9ccb83c9" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_Covid19Member_692c9971-cd28-4cec-8899-38dac55f320c" xlink:href="hg-20240930.xsd#hg_Covid19Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_UnusualOrInfrequentItemDomain_f31df4db-9968-44c6-a638-095f04554745" xlink:to="loc_hg_Covid19Member_692c9971-cd28-4cec-8899-38dac55f320c" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceContractAxis_7840bc59-9c97-4e0f-bafa-c4524358c854" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ReinsuranceContractAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseTable_6806cf03-8542-421a-b501-843be86cf7ce" xlink:to="loc_us-gaap_ReinsuranceContractAxis_7840bc59-9c97-4e0f-bafa-c4524358c854" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense_7186bf59-d8dd-49ee-84b7-96187ff43974" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseLineItems_74ba2ad9-fe7b-45a4-806f-f4090299ea99" xlink:to="loc_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense_7186bf59-d8dd-49ee-84b7-96187ff43974" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpenseNetInvestmentGainsLosses_7f4b0b8c-62a5-47ea-9680-bbf604544bb4" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredPolicyAcquisitionCostAmortizationExpenseNetInvestmentGainsLosses"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseLineItems_74ba2ad9-fe7b-45a4-806f-f4090299ea99" xlink:to="loc_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpenseNetInvestmentGainsLosses_7f4b0b8c-62a5-47ea-9680-bbf604544bb4" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseOpeningBalanceAdjustments_eb9a5e01-b3df-45c4-bd3c-1bfa42be6c5c" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseOpeningBalanceAdjustments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseLineItems_74ba2ad9-fe7b-45a4-806f-f4090299ea99" xlink:to="loc_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseOpeningBalanceAdjustments_eb9a5e01-b3df-45c4-bd3c-1bfa42be6c5c" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense_c613bdd2-76e7-48b6-84c8-466a0a513c2e" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseLineItems_74ba2ad9-fe7b-45a4-806f-f4090299ea99" xlink:to="loc_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense_c613bdd2-76e7-48b6-84c8-466a0a513c2e" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense_23a978a9-e386-45e2-9a1a-8d6741556e93" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseLineItems_74ba2ad9-fe7b-45a4-806f-f4090299ea99" xlink:to="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense_23a978a9-e386-45e2-9a1a-8d6741556e93" xlink:type="arc" order="4"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/ReserveforLossesandLossAdjustmentExpensesNarrativeDetails_1" xlink:type="simple" xlink:href="hg-20240930.xsd#ReserveforLossesandLossAdjustmentExpensesNarrativeDetails_1"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/ReserveforLossesandLossAdjustmentExpensesNarrativeDetails_1" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseLineItems_74ba2ad9-fe7b-45a4-806f-f4090299ea99" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseTable_6806cf03-8542-421a-b501-843be86cf7ce" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseLineItems_74ba2ad9-fe7b-45a4-806f-f4090299ea99" xlink:to="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseTable_6806cf03-8542-421a-b501-843be86cf7ce" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForCatastropheClaimsByCatastrophicEventAxis_565d2d18-791d-434a-879f-8598f875ec97" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LiabilityForCatastropheClaimsByCatastrophicEventAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseTable_6806cf03-8542-421a-b501-843be86cf7ce" xlink:to="loc_us-gaap_LiabilityForCatastropheClaimsByCatastrophicEventAxis_565d2d18-791d-434a-879f-8598f875ec97" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CatastrophicEventDomain_565d2d18-791d-434a-879f-8598f875ec97_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CatastrophicEventDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_LiabilityForCatastropheClaimsByCatastrophicEventAxis_565d2d18-791d-434a-879f-8598f875ec97" xlink:to="loc_us-gaap_CatastrophicEventDomain_565d2d18-791d-434a-879f-8598f875ec97_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CatastrophicEventDomain_5f66afed-2817-4947-a1f2-83005a38b149" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CatastrophicEventDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_LiabilityForCatastropheClaimsByCatastrophicEventAxis_565d2d18-791d-434a-879f-8598f875ec97" xlink:to="loc_us-gaap_CatastrophicEventDomain_5f66afed-2817-4947-a1f2-83005a38b149" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_CatastropheLossesMember_abea67ee-0b97-47be-8464-6f47cbb2edcf" xlink:href="hg-20240930.xsd#hg_CatastropheLossesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CatastrophicEventDomain_5f66afed-2817-4947-a1f2-83005a38b149" xlink:to="loc_hg_CatastropheLossesMember_abea67ee-0b97-47be-8464-6f47cbb2edcf" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncatastrophicEventAxis_0fcd3377-e2fb-4172-ad72-04c39c469abf" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NoncatastrophicEventAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseTable_6806cf03-8542-421a-b501-843be86cf7ce" xlink:to="loc_us-gaap_NoncatastrophicEventAxis_0fcd3377-e2fb-4172-ad72-04c39c469abf" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncatastrophicEventDomain_0fcd3377-e2fb-4172-ad72-04c39c469abf_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NoncatastrophicEventDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_NoncatastrophicEventAxis_0fcd3377-e2fb-4172-ad72-04c39c469abf" xlink:to="loc_us-gaap_NoncatastrophicEventDomain_0fcd3377-e2fb-4172-ad72-04c39c469abf_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncatastrophicEventDomain_fad53cec-9e77-419f-875c-eb3ce3518c34" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NoncatastrophicEventDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_NoncatastrophicEventAxis_0fcd3377-e2fb-4172-ad72-04c39c469abf" xlink:to="loc_us-gaap_NoncatastrophicEventDomain_fad53cec-9e77-419f-875c-eb3ce3518c34" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_AttritionalLossesMember_a732f51f-5c18-4692-95e6-090ed69ecd75" xlink:href="hg-20240930.xsd#hg_AttritionalLossesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_NoncatastrophicEventDomain_fad53cec-9e77-419f-875c-eb3ce3518c34" xlink:to="loc_hg_AttritionalLossesMember_a732f51f-5c18-4692-95e6-090ed69ecd75" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductOrServiceAxis_49dc80b4-53cc-4e73-a66d-21876123188f" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ProductOrServiceAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseTable_6806cf03-8542-421a-b501-843be86cf7ce" xlink:to="loc_srt_ProductOrServiceAxis_49dc80b4-53cc-4e73-a66d-21876123188f" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductsAndServicesDomain_49dc80b4-53cc-4e73-a66d-21876123188f_default" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ProductsAndServicesDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_ProductOrServiceAxis_49dc80b4-53cc-4e73-a66d-21876123188f" xlink:to="loc_srt_ProductsAndServicesDomain_49dc80b4-53cc-4e73-a66d-21876123188f_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductsAndServicesDomain_6ee89557-cb2d-4bfc-989f-0cdccac8fbd5" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ProductsAndServicesDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_ProductOrServiceAxis_49dc80b4-53cc-4e73-a66d-21876123188f" xlink:to="loc_srt_ProductsAndServicesDomain_6ee89557-cb2d-4bfc-989f-0cdccac8fbd5" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_SpecialtyContractsMember_9dc11119-ad2c-4b36-b4b9-fa5525ce5d5c" xlink:href="hg-20240930.xsd#hg_SpecialtyContractsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ProductsAndServicesDomain_6ee89557-cb2d-4bfc-989f-0cdccac8fbd5" xlink:to="loc_hg_SpecialtyContractsMember_9dc11119-ad2c-4b36-b4b9-fa5525ce5d5c" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_CasualtyLinesMember_d0159ad1-8e5c-4634-bcce-1896f17a566e" xlink:href="hg-20240930.xsd#hg_CasualtyLinesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ProductsAndServicesDomain_6ee89557-cb2d-4bfc-989f-0cdccac8fbd5" xlink:to="loc_hg_CasualtyLinesMember_d0159ad1-8e5c-4634-bcce-1896f17a566e" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_PropertyContractsMember_6d1d3a7a-d8a6-4d12-a28b-5b96f4eb3323" xlink:href="hg-20240930.xsd#hg_PropertyContractsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ProductsAndServicesDomain_6ee89557-cb2d-4bfc-989f-0cdccac8fbd5" xlink:to="loc_hg_PropertyContractsMember_6d1d3a7a-d8a6-4d12-a28b-5b96f4eb3323" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_CasualtyLinesOfBusinessMember_d0ae47f7-a5a4-4b2a-9513-644aa9e11a3a" xlink:href="hg-20240930.xsd#hg_CasualtyLinesOfBusinessMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ProductsAndServicesDomain_6ee89557-cb2d-4bfc-989f-0cdccac8fbd5" xlink:to="loc_hg_CasualtyLinesOfBusinessMember_d0ae47f7-a5a4-4b2a-9513-644aa9e11a3a" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnusualOrInfrequentItemAxis_b13bce9f-8cc2-4ba1-ba88-3bdfe49871c9" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_UnusualOrInfrequentItemAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseTable_6806cf03-8542-421a-b501-843be86cf7ce" xlink:to="loc_us-gaap_UnusualOrInfrequentItemAxis_b13bce9f-8cc2-4ba1-ba88-3bdfe49871c9" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnusualOrInfrequentItemDomain_b13bce9f-8cc2-4ba1-ba88-3bdfe49871c9_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_UnusualOrInfrequentItemDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_UnusualOrInfrequentItemAxis_b13bce9f-8cc2-4ba1-ba88-3bdfe49871c9" xlink:to="loc_us-gaap_UnusualOrInfrequentItemDomain_b13bce9f-8cc2-4ba1-ba88-3bdfe49871c9_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnusualOrInfrequentItemDomain_f31df4db-9968-44c6-a638-095f04554745" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_UnusualOrInfrequentItemDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_UnusualOrInfrequentItemAxis_b13bce9f-8cc2-4ba1-ba88-3bdfe49871c9" xlink:to="loc_us-gaap_UnusualOrInfrequentItemDomain_f31df4db-9968-44c6-a638-095f04554745" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_HurricaneHeleneMember_70617502-5fbb-4e31-9285-7ac7bd433e25" xlink:href="hg-20240930.xsd#hg_HurricaneHeleneMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_UnusualOrInfrequentItemDomain_f31df4db-9968-44c6-a638-095f04554745" xlink:to="loc_hg_HurricaneHeleneMember_70617502-5fbb-4e31-9285-7ac7bd433e25" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_BaltimoreBridgeMember_0c2822d3-8e0e-4bbd-a9e3-6bbb7826103c" xlink:href="hg-20240930.xsd#hg_BaltimoreBridgeMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_UnusualOrInfrequentItemDomain_f31df4db-9968-44c6-a638-095f04554745" xlink:to="loc_hg_BaltimoreBridgeMember_0c2822d3-8e0e-4bbd-a9e3-6bbb7826103c" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_UkrainianConflictMember_96c98372-27b4-4b9c-bc9b-8d6c9ccb83c9" xlink:href="hg-20240930.xsd#hg_UkrainianConflictMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_UnusualOrInfrequentItemDomain_f31df4db-9968-44c6-a638-095f04554745" xlink:to="loc_hg_UkrainianConflictMember_96c98372-27b4-4b9c-bc9b-8d6c9ccb83c9" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_Covid19Member_692c9971-cd28-4cec-8899-38dac55f320c" xlink:href="hg-20240930.xsd#hg_Covid19Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_UnusualOrInfrequentItemDomain_f31df4db-9968-44c6-a638-095f04554745" xlink:to="loc_hg_Covid19Member_692c9971-cd28-4cec-8899-38dac55f320c" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense_7186bf59-d8dd-49ee-84b7-96187ff43974" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseLineItems_74ba2ad9-fe7b-45a4-806f-f4090299ea99" xlink:to="loc_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense_7186bf59-d8dd-49ee-84b7-96187ff43974" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpenseNetInvestmentGainsLosses_7f4b0b8c-62a5-47ea-9680-bbf604544bb4" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredPolicyAcquisitionCostAmortizationExpenseNetInvestmentGainsLosses"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseLineItems_74ba2ad9-fe7b-45a4-806f-f4090299ea99" xlink:to="loc_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpenseNetInvestmentGainsLosses_7f4b0b8c-62a5-47ea-9680-bbf604544bb4" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseOpeningBalanceAdjustments_eb9a5e01-b3df-45c4-bd3c-1bfa42be6c5c" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseOpeningBalanceAdjustments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseLineItems_74ba2ad9-fe7b-45a4-806f-f4090299ea99" xlink:to="loc_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseOpeningBalanceAdjustments_eb9a5e01-b3df-45c4-bd3c-1bfa42be6c5c" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense_c613bdd2-76e7-48b6-84c8-466a0a513c2e" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseLineItems_74ba2ad9-fe7b-45a4-806f-f4090299ea99" xlink:to="loc_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense_c613bdd2-76e7-48b6-84c8-466a0a513c2e" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense_23a978a9-e386-45e2-9a1a-8d6741556e93" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpenseLineItems_74ba2ad9-fe7b-45a4-806f-f4090299ea99" xlink:to="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense_23a978a9-e386-45e2-9a1a-8d6741556e93" xlink:type="arc" order="4"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/SegmentReportingScheduleofSegmentReportingInformationDetails" xlink:type="simple" xlink:href="hg-20240930.xsd#SegmentReportingScheduleofSegmentReportingInformationDetails"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/SegmentReportingScheduleofSegmentReportingInformationDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SegmentReportingInformationLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_c50c6bdf-6c2b-49c5-8e9a-9a6d0e1e54db" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_c50c6bdf-6c2b-49c5-8e9a-9a6d0e1e54db" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsAxis_4cb3c73c-ece7-4d8c-b91b-9a28c7d2018c" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ConsolidationItemsAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_c50c6bdf-6c2b-49c5-8e9a-9a6d0e1e54db" xlink:to="loc_srt_ConsolidationItemsAxis_4cb3c73c-ece7-4d8c-b91b-9a28c7d2018c" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsDomain_4cb3c73c-ece7-4d8c-b91b-9a28c7d2018c_default" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ConsolidationItemsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_ConsolidationItemsAxis_4cb3c73c-ece7-4d8c-b91b-9a28c7d2018c" xlink:to="loc_srt_ConsolidationItemsDomain_4cb3c73c-ece7-4d8c-b91b-9a28c7d2018c_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsDomain_7b49eaf0-e697-4bb7-a6a5-41407387e38d" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ConsolidationItemsDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_ConsolidationItemsAxis_4cb3c73c-ece7-4d8c-b91b-9a28c7d2018c" xlink:to="loc_srt_ConsolidationItemsDomain_7b49eaf0-e697-4bb7-a6a5-41407387e38d" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingSegmentsMember_75b40976-9b66-40e6-8503-3aa8adb4980e" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OperatingSegmentsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ConsolidationItemsDomain_7b49eaf0-e697-4bb7-a6a5-41407387e38d" xlink:to="loc_us-gaap_OperatingSegmentsMember_75b40976-9b66-40e6-8503-3aa8adb4980e" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CorporateNonSegmentMember_0ef82bb9-275f-49c8-99c2-97983efe9274" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CorporateNonSegmentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ConsolidationItemsDomain_7b49eaf0-e697-4bb7-a6a5-41407387e38d" xlink:to="loc_us-gaap_CorporateNonSegmentMember_0ef82bb9-275f-49c8-99c2-97983efe9274" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementBusinessSegmentsAxis_f976f584-d099-45f0-b97f-7474e660c139" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementBusinessSegmentsAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_c50c6bdf-6c2b-49c5-8e9a-9a6d0e1e54db" xlink:to="loc_us-gaap_StatementBusinessSegmentsAxis_f976f584-d099-45f0-b97f-7474e660c139" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain_f976f584-d099-45f0-b97f-7474e660c139_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SegmentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis_f976f584-d099-45f0-b97f-7474e660c139" xlink:to="loc_us-gaap_SegmentDomain_f976f584-d099-45f0-b97f-7474e660c139_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain_c265e409-d780-4033-98e5-6e71773df7ea" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SegmentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis_f976f584-d099-45f0-b97f-7474e660c139" xlink:to="loc_us-gaap_SegmentDomain_c265e409-d780-4033-98e5-6e71773df7ea" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_InternationalSegmentMember_793a8337-0b82-4354-9c65-c9aa4c1f6df7" xlink:href="hg-20240930.xsd#hg_InternationalSegmentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentDomain_c265e409-d780-4033-98e5-6e71773df7ea" xlink:to="loc_hg_InternationalSegmentMember_793a8337-0b82-4354-9c65-c9aa4c1f6df7" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_BermudaSegmentMember_b1112995-1b29-4903-8180-220fab5b91e5" xlink:href="hg-20240930.xsd#hg_BermudaSegmentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentDomain_c265e409-d780-4033-98e5-6e71773df7ea" xlink:to="loc_hg_BermudaSegmentMember_b1112995-1b29-4903-8180-220fab5b91e5" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfReportableSegments_f0e1cf6b-6631-490d-add7-a2ebd86c1c5a" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NumberOfReportableSegments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_us-gaap_NumberOfReportableSegments_f0e1cf6b-6631-490d-add7-a2ebd86c1c5a" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsWrittenGross_02c16b8c-0f02-4582-8315-70b10d4f5ecd" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PremiumsWrittenGross"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_us-gaap_PremiumsWrittenGross_02c16b8c-0f02-4582-8315-70b10d4f5ecd" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsWrittenNet_44efb3f4-92e0-475f-9663-03b1aa70ed61" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PremiumsWrittenNet"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_us-gaap_PremiumsWrittenNet_44efb3f4-92e0-475f-9663-03b1aa70ed61" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsEarnedNet_76066d39-1318-4aaf-ac5b-7019c3f28f14" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PremiumsEarnedNet"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_us-gaap_PremiumsEarnedNet_76066d39-1318-4aaf-ac5b-7019c3f28f14" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InsuranceAgencyManagementFee_e9b85672-51e5-42d6-9fc8-f08daff118af" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InsuranceAgencyManagementFee"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_us-gaap_InsuranceAgencyManagementFee_e9b85672-51e5-42d6-9fc8-f08daff118af" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseIncurredClaims1_91e029fd-6e17-4b00-a12a-ffe86f4c27f2" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseIncurredClaims1"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseIncurredClaims1_91e029fd-6e17-4b00-a12a-ffe86f4c27f2" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense_33d31c7c-28d3-4a2c-9362-031509033d0d" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense_33d31c7c-28d3-4a2c-9362-031509033d0d" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherUnderwritingExpense_bc5bf2ca-821d-4f78-b44b-25b553e6ec13" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherUnderwritingExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_us-gaap_OtherUnderwritingExpense_bc5bf2ca-821d-4f78-b44b-25b553e6ec13" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_UnderwritingIncomeLossNet_b9821f9c-f8c6-4581-97b1-9b95fe066b67" xlink:href="hg-20240930.xsd#hg_UnderwritingIncomeLossNet"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_hg_UnderwritingIncomeLossNet_b9821f9c-f8c6-4581-97b1-9b95fe066b67" xlink:type="arc" order="8"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnInvestments_6b16f271-7a53-4fa8-94fa-c78cb4fe192e" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GainLossOnInvestments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_us-gaap_GainLossOnInvestments_6b16f271-7a53-4fa8-94fa-c78cb4fe192e" xlink:type="arc" order="9"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeNet_d235bb57-60cb-4b72-b7f7-b7632d2aae72" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InvestmentIncomeNet"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_us-gaap_InvestmentIncomeNet_d235bb57-60cb-4b72-b7f7-b7632d2aae72" xlink:type="arc" order="10"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_OtherIncomeLossExcludingThirdPartyFeeIncome_6d473d30-595c-48e1-a0fe-a548866feb16" xlink:href="hg-20240930.xsd#hg_OtherIncomeLossExcludingThirdPartyFeeIncome"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_hg_OtherIncomeLossExcludingThirdPartyFeeIncome_6d473d30-595c-48e1-a0fe-a548866feb16" xlink:type="arc" order="11"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax_6c75c364-550b-445e-bd0f-524ab38eb8d2" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ForeignCurrencyTransactionGainLossBeforeTax"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_us-gaap_ForeignCurrencyTransactionGainLossBeforeTax_6c75c364-550b-445e-bd0f-524ab38eb8d2" xlink:type="arc" order="12"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeneralAndAdministrativeExpense_2105695a-3c9a-4669-92fb-a7a59949e0d8" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GeneralAndAdministrativeExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_us-gaap_GeneralAndAdministrativeExpense_2105695a-3c9a-4669-92fb-a7a59949e0d8" xlink:type="arc" order="13"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfIntangibleAssets_c99816bc-35df-4476-8c8e-c5b65f0d1733" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AmortizationOfIntangibleAssets"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_us-gaap_AmortizationOfIntangibleAssets_c99816bc-35df-4476-8c8e-c5b65f0d1733" xlink:type="arc" order="14"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpense_ce1f0105-9b6b-499d-9c34-488454cd1ece" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InterestExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_us-gaap_InterestExpense_ce1f0105-9b6b-499d-9c34-488454cd1ece" xlink:type="arc" order="15"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_4fe66185-ed60-4e57-abdf-f0f88a4b36d8" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_4fe66185-ed60-4e57-abdf-f0f88a4b36d8" xlink:type="arc" order="16"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefit_df8f4e97-e1b8-40d3-8579-5e2dd4c3065f" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_us-gaap_IncomeTaxExpenseBenefit_df8f4e97-e1b8-40d3-8579-5e2dd4c3065f" xlink:type="arc" order="17"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss_8074f6f3-c8e8-4554-9986-2068e6477737" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ProfitLoss"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_us-gaap_ProfitLoss_8074f6f3-c8e8-4554-9986-2068e6477737" xlink:type="arc" order="18"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAttributableToRedeemableNoncontrollingInterest_eda03a49-adba-4967-9792-1339accd89d5" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetIncomeLossAttributableToRedeemableNoncontrollingInterest"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_us-gaap_NetIncomeLossAttributableToRedeemableNoncontrollingInterest_eda03a49-adba-4967-9792-1339accd89d5" xlink:type="arc" order="19"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest_dadcf742-fb21-4f3f-a5f1-e46457c718a1" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest_dadcf742-fb21-4f3f-a5f1-e46457c718a1" xlink:type="arc" order="20"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_AttritionalLossRatioCurrentYear_e379d9dd-234f-4753-b7ba-9e11f9389e9b" xlink:href="hg-20240930.xsd#hg_AttritionalLossRatioCurrentYear"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_hg_AttritionalLossRatioCurrentYear_e379d9dd-234f-4753-b7ba-9e11f9389e9b" xlink:type="arc" order="21"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_AttritionalLossRatioPriorYearDevelopment_c6c14a29-d630-419c-b7c1-e69fb4b9884d" xlink:href="hg-20240930.xsd#hg_AttritionalLossRatioPriorYearDevelopment"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_hg_AttritionalLossRatioPriorYearDevelopment_c6c14a29-d630-419c-b7c1-e69fb4b9884d" xlink:type="arc" order="22"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_CatastropheLossRatioCurrentYear_496e2a59-bd8c-4010-ab8d-a669444e911f" xlink:href="hg-20240930.xsd#hg_CatastropheLossRatioCurrentYear"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_hg_CatastropheLossRatioCurrentYear_496e2a59-bd8c-4010-ab8d-a669444e911f" xlink:type="arc" order="23"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_CatastropheLossRatioPriorYearDevelopment_53334b2b-cf15-4aab-90dc-f2e1ef416f17" xlink:href="hg-20240930.xsd#hg_CatastropheLossRatioPriorYearDevelopment"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_hg_CatastropheLossRatioPriorYearDevelopment_53334b2b-cf15-4aab-90dc-f2e1ef416f17" xlink:type="arc" order="24"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossRatio_7cf82e93-7d2f-4bb6-937b-9119c613d7c2" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LossRatio"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_us-gaap_LossRatio_7cf82e93-7d2f-4bb6-937b-9119c613d7c2" xlink:type="arc" order="25"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AcquisitionCostRatio_0172bd7b-95f5-456f-95b5-2859e898fc7f" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AcquisitionCostRatio"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_us-gaap_AcquisitionCostRatio_0172bd7b-95f5-456f-95b5-2859e898fc7f" xlink:type="arc" order="26"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnderwritingExpenseRatio_38f82d16-f8c9-4e3f-b953-eaff7cfdba7e" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_UnderwritingExpenseRatio"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_us-gaap_UnderwritingExpenseRatio_38f82d16-f8c9-4e3f-b953-eaff7cfdba7e" xlink:type="arc" order="27"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CombinedRatio_1545dc85-a956-4ef1-bb81-7d7c4437b004" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CombinedRatio"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_804d29d5-fc30-493d-9340-12e5a1abcad4" xlink:to="loc_us-gaap_CombinedRatio_1545dc85-a956-4ef1-bb81-7d7c4437b004" xlink:type="arc" order="28"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/SegmentReportingScheduleofGrossPremiumsWrittenbyGeographicalLocationofSubsidiariesDetails" xlink:type="simple" xlink:href="hg-20240930.xsd#SegmentReportingScheduleofGrossPremiumsWrittenbyGeographicalLocationofSubsidiariesDetails"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/SegmentReportingScheduleofGrossPremiumsWrittenbyGeographicalLocationofSubsidiariesDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems_e4e058a5-f982-4acc-898f-3940b1ee329a" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsTable_754b1602-7786-4d36-9660-366e6d05109f" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems_e4e058a5-f982-4acc-898f-3940b1ee329a" xlink:to="loc_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsTable_754b1602-7786-4d36-9660-366e6d05109f" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StatementGeographicalAxis_4f27dde2-05bb-4b6c-9276-0522a7d15d3f" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_StatementGeographicalAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsTable_754b1602-7786-4d36-9660-366e6d05109f" xlink:to="loc_srt_StatementGeographicalAxis_4f27dde2-05bb-4b6c-9276-0522a7d15d3f" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_SegmentGeographicalDomain_4f27dde2-05bb-4b6c-9276-0522a7d15d3f_default" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_SegmentGeographicalDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_StatementGeographicalAxis_4f27dde2-05bb-4b6c-9276-0522a7d15d3f" xlink:to="loc_srt_SegmentGeographicalDomain_4f27dde2-05bb-4b6c-9276-0522a7d15d3f_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_SegmentGeographicalDomain_7d5e564c-5c50-43ae-89fd-b8442f7d6b93" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_SegmentGeographicalDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_StatementGeographicalAxis_4f27dde2-05bb-4b6c-9276-0522a7d15d3f" xlink:to="loc_srt_SegmentGeographicalDomain_7d5e564c-5c50-43ae-89fd-b8442f7d6b93" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_InternationalSegmentMember_153780d8-c2de-4415-9a11-bb8107f75eb9" xlink:href="hg-20240930.xsd#hg_InternationalSegmentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_SegmentGeographicalDomain_7d5e564c-5c50-43ae-89fd-b8442f7d6b93" xlink:to="loc_hg_InternationalSegmentMember_153780d8-c2de-4415-9a11-bb8107f75eb9" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_country_GB_70e3ae81-6cb2-4958-b2f4-d98e9e0644d7" xlink:href="https://xbrl.sec.gov/country/2024/country-2024.xsd#country_GB"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_hg_InternationalSegmentMember_153780d8-c2de-4415-9a11-bb8107f75eb9" xlink:to="loc_country_GB_70e3ae81-6cb2-4958-b2f4-d98e9e0644d7" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_country_IE_31dc5ee0-98a9-4c48-9c13-ff1125e38611" xlink:href="https://xbrl.sec.gov/country/2024/country-2024.xsd#country_IE"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_hg_InternationalSegmentMember_153780d8-c2de-4415-9a11-bb8107f75eb9" xlink:to="loc_country_IE_31dc5ee0-98a9-4c48-9c13-ff1125e38611" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_country_US_a6044cba-e3fd-4e0c-89e4-531b1d1d9ed3" xlink:href="https://xbrl.sec.gov/country/2024/country-2024.xsd#country_US"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_hg_InternationalSegmentMember_153780d8-c2de-4415-9a11-bb8107f75eb9" xlink:to="loc_country_US_a6044cba-e3fd-4e0c-89e4-531b1d1d9ed3" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_country_BM_bc41d9e5-0dc3-47e9-b69b-db4a9c649019" xlink:href="https://xbrl.sec.gov/country/2024/country-2024.xsd#country_BM"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_SegmentGeographicalDomain_7d5e564c-5c50-43ae-89fd-b8442f7d6b93" xlink:to="loc_country_BM_bc41d9e5-0dc3-47e9-b69b-db4a9c649019" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsWrittenGross_b272a7c4-6874-4486-b37a-608432cc71cd" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PremiumsWrittenGross"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems_e4e058a5-f982-4acc-898f-3940b1ee329a" xlink:to="loc_us-gaap_PremiumsWrittenGross_b272a7c4-6874-4486-b37a-608432cc71cd" xlink:type="arc" order="0"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/DebtandCreditFacilitiesNarrativeDetails" xlink:type="simple" xlink:href="hg-20240930.xsd#DebtandCreditFacilitiesNarrativeDetails"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/DebtandCreditFacilitiesNarrativeDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityLineItems_1b641888-3d09-49a1-92e4-e162625cf638" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LineOfCreditFacilityLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityTable_684ff4fa-0aff-4361-98c7-4b0d3b39c6ae" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LineOfCreditFacilityTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_LineOfCreditFacilityLineItems_1b641888-3d09-49a1-92e4-e162625cf638" xlink:to="loc_us-gaap_LineOfCreditFacilityTable_684ff4fa-0aff-4361-98c7-4b0d3b39c6ae" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis_60d51465-9903-4c60-bff0-296fdeba8085" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_LineOfCreditFacilityTable_684ff4fa-0aff-4361-98c7-4b0d3b39c6ae" xlink:to="loc_us-gaap_LongtermDebtTypeAxis_60d51465-9903-4c60-bff0-296fdeba8085" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain_60d51465-9903-4c60-bff0-296fdeba8085_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_LongtermDebtTypeAxis_60d51465-9903-4c60-bff0-296fdeba8085" xlink:to="loc_us-gaap_LongtermDebtTypeDomain_60d51465-9903-4c60-bff0-296fdeba8085_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain_67eef189-bc32-40c0-8ed7-e08ca0bee742" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_LongtermDebtTypeAxis_60d51465-9903-4c60-bff0-296fdeba8085" xlink:to="loc_us-gaap_LongtermDebtTypeDomain_67eef189-bc32-40c0-8ed7-e08ca0bee742" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnsecuredDebtMember_ec08c494-4b2a-47ba-b829-97daf3c76ea3" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_UnsecuredDebtMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LongtermDebtTypeDomain_67eef189-bc32-40c0-8ed7-e08ca0bee742" xlink:to="loc_us-gaap_UnsecuredDebtMember_ec08c494-4b2a-47ba-b829-97daf3c76ea3" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditMember_630014b0-c7d3-4671-8d20-81df30551443" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LineOfCreditMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LongtermDebtTypeDomain_67eef189-bc32-40c0-8ed7-e08ca0bee742" xlink:to="loc_us-gaap_LineOfCreditMember_630014b0-c7d3-4671-8d20-81df30551443" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis_0d549cbb-d2a5-49aa-b217-d4c8e7a147d5" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_LineOfCreditFacilityTable_684ff4fa-0aff-4361-98c7-4b0d3b39c6ae" xlink:to="loc_us-gaap_DebtInstrumentAxis_0d549cbb-d2a5-49aa-b217-d4c8e7a147d5" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain_0d549cbb-d2a5-49aa-b217-d4c8e7a147d5_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_DebtInstrumentAxis_0d549cbb-d2a5-49aa-b217-d4c8e7a147d5" xlink:to="loc_us-gaap_DebtInstrumentNameDomain_0d549cbb-d2a5-49aa-b217-d4c8e7a147d5_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain_4d1b9a6a-a0b8-4c1c-9166-f0bee03c76ff" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_DebtInstrumentAxis_0d549cbb-d2a5-49aa-b217-d4c8e7a147d5" xlink:to="loc_us-gaap_DebtInstrumentNameDomain_4d1b9a6a-a0b8-4c1c-9166-f0bee03c76ff" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_TermLoanMember_58974999-6d41-402b-a6be-b4f1bbed4bfd" xlink:href="hg-20240930.xsd#hg_TermLoanMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentNameDomain_4d1b9a6a-a0b8-4c1c-9166-f0bee03c76ff" xlink:to="loc_hg_TermLoanMember_58974999-6d41-402b-a6be-b4f1bbed4bfd" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_UncommittedSecuredLetterOfCreditFacilityMember_42794799-6c1b-4f64-bbbe-f826934ece7c" xlink:href="hg-20240930.xsd#hg_UncommittedSecuredLetterOfCreditFacilityMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentNameDomain_4d1b9a6a-a0b8-4c1c-9166-f0bee03c76ff" xlink:to="loc_hg_UncommittedSecuredLetterOfCreditFacilityMember_42794799-6c1b-4f64-bbbe-f826934ece7c" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_UnsecuredFacilityMember_1f87c1bd-6afb-4737-9a62-3dfd7837ba39" xlink:href="hg-20240930.xsd#hg_UnsecuredFacilityMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentNameDomain_4d1b9a6a-a0b8-4c1c-9166-f0bee03c76ff" xlink:to="loc_hg_UnsecuredFacilityMember_1f87c1bd-6afb-4737-9a62-3dfd7837ba39" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_BankOfMontrealLetterOfCreditFacilityMember_fd702e92-7061-452a-80fd-823416797084" xlink:href="hg-20240930.xsd#hg_BankOfMontrealLetterOfCreditFacilityMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentNameDomain_4d1b9a6a-a0b8-4c1c-9166-f0bee03c76ff" xlink:to="loc_hg_BankOfMontrealLetterOfCreditFacilityMember_fd702e92-7061-452a-80fd-823416797084" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_UBSLetterOfCreditFacilityMember_6cae570d-4a84-41b5-a1bd-0f209cb0c94f" xlink:href="hg-20240930.xsd#hg_UBSLetterOfCreditFacilityMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentNameDomain_4d1b9a6a-a0b8-4c1c-9166-f0bee03c76ff" xlink:to="loc_hg_UBSLetterOfCreditFacilityMember_6cae570d-4a84-41b5-a1bd-0f209cb0c94f" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_UnsecuredFacilityLloydsMember_42e43a79-0e2e-40de-8a0b-25c57b2b1797" xlink:href="hg-20240930.xsd#hg_UnsecuredFacilityLloydsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentNameDomain_4d1b9a6a-a0b8-4c1c-9166-f0bee03c76ff" xlink:to="loc_hg_UnsecuredFacilityLloydsMember_42e43a79-0e2e-40de-8a0b-25c57b2b1797" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityAxis_df8a41c4-9d64-4e32-a657-e6b4dbe46ece" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CreditFacilityAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_LineOfCreditFacilityTable_684ff4fa-0aff-4361-98c7-4b0d3b39c6ae" xlink:to="loc_us-gaap_CreditFacilityAxis_df8a41c4-9d64-4e32-a657-e6b4dbe46ece" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityDomain_df8a41c4-9d64-4e32-a657-e6b4dbe46ece_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CreditFacilityDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_CreditFacilityAxis_df8a41c4-9d64-4e32-a657-e6b4dbe46ece" xlink:to="loc_us-gaap_CreditFacilityDomain_df8a41c4-9d64-4e32-a657-e6b4dbe46ece_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityDomain_6ea3a4b4-d177-443c-a622-0fee4d9c6601" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CreditFacilityDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_CreditFacilityAxis_df8a41c4-9d64-4e32-a657-e6b4dbe46ece" xlink:to="loc_us-gaap_CreditFacilityDomain_6ea3a4b4-d177-443c-a622-0fee4d9c6601" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LetterOfCreditMember_ab608843-56f4-471e-a886-c1e5f0c6e784" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LetterOfCreditMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CreditFacilityDomain_6ea3a4b4-d177-443c-a622-0fee4d9c6601" xlink:to="loc_us-gaap_LetterOfCreditMember_ab608843-56f4-471e-a886-c1e5f0c6e784" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevolvingCreditFacilityMember_c00802fa-547f-4093-9114-a204b15e256a" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RevolvingCreditFacilityMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CreditFacilityDomain_6ea3a4b4-d177-443c-a622-0fee4d9c6601" xlink:to="loc_us-gaap_RevolvingCreditFacilityMember_c00802fa-547f-4093-9114-a204b15e256a" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeAxis_6ec58567-edef-448a-9fd2-ee46b4df2625" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsequentEventTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_LineOfCreditFacilityTable_684ff4fa-0aff-4361-98c7-4b0d3b39c6ae" xlink:to="loc_us-gaap_SubsequentEventTypeAxis_6ec58567-edef-448a-9fd2-ee46b4df2625" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeDomain_6ec58567-edef-448a-9fd2-ee46b4df2625_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsequentEventTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_SubsequentEventTypeAxis_6ec58567-edef-448a-9fd2-ee46b4df2625" xlink:to="loc_us-gaap_SubsequentEventTypeDomain_6ec58567-edef-448a-9fd2-ee46b4df2625_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeDomain_c7aa91e4-c772-44d3-9d57-237c823ea63b" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsequentEventTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_SubsequentEventTypeAxis_6ec58567-edef-448a-9fd2-ee46b4df2625" xlink:to="loc_us-gaap_SubsequentEventTypeDomain_c7aa91e4-c772-44d3-9d57-237c823ea63b" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventMember_5bb4e09f-f6f1-4ca0-8d41-3447ccbba47e" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsequentEventMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SubsequentEventTypeDomain_c7aa91e4-c772-44d3-9d57-237c823ea63b" xlink:to="loc_us-gaap_SubsequentEventMember_5bb4e09f-f6f1-4ca0-8d41-3447ccbba47e" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFaceAmount_48e77c1c-36d9-4325-915c-6d538089a754" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentFaceAmount"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LineOfCreditFacilityLineItems_1b641888-3d09-49a1-92e4-e162625cf638" xlink:to="loc_us-gaap_DebtInstrumentFaceAmount_48e77c1c-36d9-4325-915c-6d538089a754" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_DebtInstrumentInterestRateIncreaseDecreaseInEventOfDefault_cd3aa6d1-b7c9-4fae-b4ef-a222f751573d" xlink:href="hg-20240930.xsd#hg_DebtInstrumentInterestRateIncreaseDecreaseInEventOfDefault"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LineOfCreditFacilityLineItems_1b641888-3d09-49a1-92e4-e162625cf638" xlink:to="loc_hg_DebtInstrumentInterestRateIncreaseDecreaseInEventOfDefault_cd3aa6d1-b7c9-4fae-b4ef-a222f751573d" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfFinancingCosts_8171cade-478d-4483-a494-b5c56049039b" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AmortizationOfFinancingCosts"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LineOfCreditFacilityLineItems_1b641888-3d09-49a1-92e4-e162625cf638" xlink:to="loc_us-gaap_AmortizationOfFinancingCosts_8171cade-478d-4483-a494-b5c56049039b" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_9271c60a-9ee2-4c5f-a4ec-ccf8f6b7784e" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LineOfCreditFacilityLineItems_1b641888-3d09-49a1-92e4-e162625cf638" xlink:to="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_9271c60a-9ee2-4c5f-a4ec-ccf8f6b7784e" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCredit_474d2d3c-7133-4918-9ecc-27a1034c6e01" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LineOfCredit"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LineOfCreditFacilityLineItems_1b641888-3d09-49a1-92e4-e162625cf638" xlink:to="loc_us-gaap_LineOfCredit_474d2d3c-7133-4918-9ecc-27a1034c6e01" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage_2da04eee-df69-4e41-9a21-5e698b5ebd7d" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LineOfCreditFacilityLineItems_1b641888-3d09-49a1-92e4-e162625cf638" xlink:to="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage_2da04eee-df69-4e41-9a21-5e698b5ebd7d" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_2c4b29cd-105b-40c5-894d-e108578b25ea" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentBasisSpreadOnVariableRate1"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LineOfCreditFacilityLineItems_1b641888-3d09-49a1-92e4-e162625cf638" xlink:to="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_2c4b29cd-105b-40c5-894d-e108578b25ea" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage_c88d7787-2ab5-4e05-a098-b62aa860af94" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LineOfCreditFacilityLineItems_1b641888-3d09-49a1-92e4-e162625cf638" xlink:to="loc_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage_c88d7787-2ab5-4e05-a098-b62aa860af94" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityCommitmentFeePercentage_7a398a7a-f95e-4ae5-b85a-30804ba98b36" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LineOfCreditFacilityCommitmentFeePercentage"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LineOfCreditFacilityLineItems_1b641888-3d09-49a1-92e4-e162625cf638" xlink:to="loc_us-gaap_LineOfCreditFacilityCommitmentFeePercentage_7a398a7a-f95e-4ae5-b85a-30804ba98b36" xlink:type="arc" order="8"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtTerm_6e31249d-f2b8-430a-8af2-ee71e2e8b6f4" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LongTermDebtTerm"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LineOfCreditFacilityLineItems_1b641888-3d09-49a1-92e4-e162625cf638" xlink:to="loc_us-gaap_LongTermDebtTerm_6e31249d-f2b8-430a-8af2-ee71e2e8b6f4" xlink:type="arc" order="9"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpense_1762ba4a-e08d-4ddf-9a57-681b8b94d466" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InterestExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LineOfCreditFacilityLineItems_1b641888-3d09-49a1-92e4-e162625cf638" xlink:to="loc_us-gaap_InterestExpense_1762ba4a-e08d-4ddf-9a57-681b8b94d466" xlink:type="arc" order="10"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/DebtandCreditFacilitiesScheduleofCompanyComplianceDetails" xlink:type="simple" xlink:href="hg-20240930.xsd#DebtandCreditFacilitiesScheduleofCompanyComplianceDetails"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/DebtandCreditFacilitiesScheduleofCompanyComplianceDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityLineItems_99e3d7f2-cb01-4530-9404-2b4f4e14eb7c" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LineOfCreditFacilityLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityTable_a4ec4b46-eccd-41fb-86ff-3265354cd674" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LineOfCreditFacilityTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_LineOfCreditFacilityLineItems_99e3d7f2-cb01-4530-9404-2b4f4e14eb7c" xlink:to="loc_us-gaap_LineOfCreditFacilityTable_a4ec4b46-eccd-41fb-86ff-3265354cd674" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis_5a6dccd5-381f-4b67-b505-e2a5a1c35fb5" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_LineOfCreditFacilityTable_a4ec4b46-eccd-41fb-86ff-3265354cd674" xlink:to="loc_us-gaap_DebtInstrumentAxis_5a6dccd5-381f-4b67-b505-e2a5a1c35fb5" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain_5a6dccd5-381f-4b67-b505-e2a5a1c35fb5_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_DebtInstrumentAxis_5a6dccd5-381f-4b67-b505-e2a5a1c35fb5" xlink:to="loc_us-gaap_DebtInstrumentNameDomain_5a6dccd5-381f-4b67-b505-e2a5a1c35fb5_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain_e0ea9957-ab66-4bcb-b5b4-ac2dc25e4fc9" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_DebtInstrumentAxis_5a6dccd5-381f-4b67-b505-e2a5a1c35fb5" xlink:to="loc_us-gaap_DebtInstrumentNameDomain_e0ea9957-ab66-4bcb-b5b4-ac2dc25e4fc9" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_TermLoanMember_7ec35e10-03f9-48a1-a518-479e3bca5a07" xlink:href="hg-20240930.xsd#hg_TermLoanMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentNameDomain_e0ea9957-ab66-4bcb-b5b4-ac2dc25e4fc9" xlink:to="loc_hg_TermLoanMember_7ec35e10-03f9-48a1-a518-479e3bca5a07" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis_d7076650-aa29-429e-86a9-7a9d1b7cfc12" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_LineOfCreditFacilityTable_a4ec4b46-eccd-41fb-86ff-3265354cd674" xlink:to="loc_us-gaap_LongtermDebtTypeAxis_d7076650-aa29-429e-86a9-7a9d1b7cfc12" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain_d7076650-aa29-429e-86a9-7a9d1b7cfc12_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_LongtermDebtTypeAxis_d7076650-aa29-429e-86a9-7a9d1b7cfc12" xlink:to="loc_us-gaap_LongtermDebtTypeDomain_d7076650-aa29-429e-86a9-7a9d1b7cfc12_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain_2899d9d9-a272-49a3-b1be-20840b9d10c8" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_LongtermDebtTypeAxis_d7076650-aa29-429e-86a9-7a9d1b7cfc12" xlink:to="loc_us-gaap_LongtermDebtTypeDomain_2899d9d9-a272-49a3-b1be-20840b9d10c8" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnsecuredDebtMember_300155d8-529c-40ee-bd73-fbbd5c2c4a60" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_UnsecuredDebtMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LongtermDebtTypeDomain_2899d9d9-a272-49a3-b1be-20840b9d10c8" xlink:to="loc_us-gaap_UnsecuredDebtMember_300155d8-529c-40ee-bd73-fbbd5c2c4a60" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentCarryingAmount_f0adc881-8daf-40f5-93df-e9e8ab6c05c8" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentCarryingAmount"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LineOfCreditFacilityLineItems_99e3d7f2-cb01-4530-9404-2b4f4e14eb7c" xlink:to="loc_us-gaap_DebtInstrumentCarryingAmount_f0adc881-8daf-40f5-93df-e9e8ab6c05c8" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtFairValue_8080d51a-0b5f-4e48-8178-56e035745ad0" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LongTermDebtFairValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LineOfCreditFacilityLineItems_99e3d7f2-cb01-4530-9404-2b4f4e14eb7c" xlink:to="loc_us-gaap_LongTermDebtFairValue_8080d51a-0b5f-4e48-8178-56e035745ad0" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredFinanceCostsNet_85332e8b-7f0f-482c-8db7-d796f1d7a131" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DeferredFinanceCostsNet"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LineOfCreditFacilityLineItems_99e3d7f2-cb01-4530-9404-2b4f4e14eb7c" xlink:to="loc_us-gaap_DeferredFinanceCostsNet_85332e8b-7f0f-482c-8db7-d796f1d7a131" xlink:type="arc" order="2"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/DebtandCreditFacilitiesScheduleofCreditFacilitiesDetails" xlink:type="simple" xlink:href="hg-20240930.xsd#DebtandCreditFacilitiesScheduleofCreditFacilitiesDetails"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/DebtandCreditFacilitiesScheduleofCreditFacilitiesDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityLineItems_ed8fe078-417f-4e25-a0cf-f22f4b9e5ec5" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LineOfCreditFacilityLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityTable_99282081-3587-4dce-b22a-9a3165c15e60" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LineOfCreditFacilityTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_LineOfCreditFacilityLineItems_ed8fe078-417f-4e25-a0cf-f22f4b9e5ec5" xlink:to="loc_us-gaap_LineOfCreditFacilityTable_99282081-3587-4dce-b22a-9a3165c15e60" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PledgingPurposeAxis_c490670a-eaaf-4f30-9e5a-15b038021fa7" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PledgingPurposeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_LineOfCreditFacilityTable_99282081-3587-4dce-b22a-9a3165c15e60" xlink:to="loc_us-gaap_PledgingPurposeAxis_c490670a-eaaf-4f30-9e5a-15b038021fa7" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PledgingPurposeDomain_c490670a-eaaf-4f30-9e5a-15b038021fa7_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PledgingPurposeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_PledgingPurposeAxis_c490670a-eaaf-4f30-9e5a-15b038021fa7" xlink:to="loc_us-gaap_PledgingPurposeDomain_c490670a-eaaf-4f30-9e5a-15b038021fa7_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PledgingPurposeDomain_787a4fec-686d-4996-825f-bc83fbfa9af5" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PledgingPurposeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_PledgingPurposeAxis_c490670a-eaaf-4f30-9e5a-15b038021fa7" xlink:to="loc_us-gaap_PledgingPurposeDomain_787a4fec-686d-4996-825f-bc83fbfa9af5" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_TSHamiltonFundMember_8e7092f4-dee4-4944-8ff2-cedbf381cb26" xlink:href="hg-20240930.xsd#hg_TSHamiltonFundMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_PledgingPurposeDomain_787a4fec-686d-4996-825f-bc83fbfa9af5" xlink:to="loc_hg_TSHamiltonFundMember_8e7092f4-dee4-4944-8ff2-cedbf381cb26" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_FixedIncomePortfolioMember_c55cb479-a18f-45e9-96cd-026daa65cd91" xlink:href="hg-20240930.xsd#hg_FixedIncomePortfolioMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_PledgingPurposeDomain_787a4fec-686d-4996-825f-bc83fbfa9af5" xlink:to="loc_hg_FixedIncomePortfolioMember_c55cb479-a18f-45e9-96cd-026daa65cd91" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashMember_c1201698-2f41-488e-b7c4-15474577fee6" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CashMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_PledgingPurposeDomain_787a4fec-686d-4996-825f-bc83fbfa9af5" xlink:to="loc_us-gaap_CashMember_c1201698-2f41-488e-b7c4-15474577fee6" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_123cb755-0b46-45c4-8fd8-124d4a6f2d5e" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LineOfCreditFacilityLineItems_ed8fe078-417f-4e25-a0cf-f22f4b9e5ec5" xlink:to="loc_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_123cb755-0b46-45c4-8fd8-124d4a6f2d5e" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCredit_73ddb5d5-43bb-44eb-bb7b-d16a35834186" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LineOfCredit"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LineOfCreditFacilityLineItems_ed8fe078-417f-4e25-a0cf-f22f4b9e5ec5" xlink:to="loc_us-gaap_LineOfCredit_73ddb5d5-43bb-44eb-bb7b-d16a35834186" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentCollateralAmount_c30398e4-f3de-498f-b695-adb2114fe270" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentCollateralAmount"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LineOfCreditFacilityLineItems_ed8fe078-417f-4e25-a0cf-f22f4b9e5ec5" xlink:to="loc_us-gaap_DebtInstrumentCollateralAmount_c30398e4-f3de-498f-b695-adb2114fe270" xlink:type="arc" order="2"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/ShareCapitalScheduleofShareCapitalDetails" xlink:type="simple" xlink:href="hg-20240930.xsd#ShareCapitalScheduleofShareCapitalDetails"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/ShareCapitalScheduleofShareCapitalDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockLineItems_ae71f6dd-3ee7-4301-9a08-e8add6ab5697" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ClassOfStockLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockByClassTable_46df2c46-8900-4439-8a22-29779f3295d2" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfStockByClassTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ClassOfStockLineItems_ae71f6dd-3ee7-4301-9a08-e8add6ab5697" xlink:to="loc_us-gaap_ScheduleOfStockByClassTable_46df2c46-8900-4439-8a22-29779f3295d2" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementClassOfStockAxis_ca84ad57-2507-46fd-b5f1-9b9d839fe97a" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementClassOfStockAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfStockByClassTable_46df2c46-8900-4439-8a22-29779f3295d2" xlink:to="loc_us-gaap_StatementClassOfStockAxis_ca84ad57-2507-46fd-b5f1-9b9d839fe97a" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain_ca84ad57-2507-46fd-b5f1-9b9d839fe97a_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ClassOfStockDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_StatementClassOfStockAxis_ca84ad57-2507-46fd-b5f1-9b9d839fe97a" xlink:to="loc_us-gaap_ClassOfStockDomain_ca84ad57-2507-46fd-b5f1-9b9d839fe97a_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain_7537fdd3-2c49-48ed-b60d-502a352765c7" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ClassOfStockDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_StatementClassOfStockAxis_ca84ad57-2507-46fd-b5f1-9b9d839fe97a" xlink:to="loc_us-gaap_ClassOfStockDomain_7537fdd3-2c49-48ed-b60d-502a352765c7" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassAMember_e448b362-1a4c-4eae-a6c7-070d6fb5f62b" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonClassAMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockDomain_7537fdd3-2c49-48ed-b60d-502a352765c7" xlink:to="loc_us-gaap_CommonClassAMember_e448b362-1a4c-4eae-a6c7-070d6fb5f62b" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassBMember_73a8b8dd-f7fa-449d-8198-afd80ef48fb2" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonClassBMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockDomain_7537fdd3-2c49-48ed-b60d-502a352765c7" xlink:to="loc_us-gaap_CommonClassBMember_73a8b8dd-f7fa-449d-8198-afd80ef48fb2" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassCMember_4342fecf-8c81-4cb5-bef5-560e02a5afff" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonClassCMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockDomain_7537fdd3-2c49-48ed-b60d-502a352765c7" xlink:to="loc_us-gaap_CommonClassCMember_4342fecf-8c81-4cb5-bef5-560e02a5afff" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockParOrStatedValuePerShare_cecc3dbf-c594-44f3-99c5-9f3c07add187" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockParOrStatedValuePerShare"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockLineItems_ae71f6dd-3ee7-4301-9a08-e8add6ab5697" xlink:to="loc_us-gaap_CommonStockParOrStatedValuePerShare_cecc3dbf-c594-44f3-99c5-9f3c07add187" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorized_f5211732-bf62-49b5-ba19-39ccf10caec4" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockSharesAuthorized"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockLineItems_ae71f6dd-3ee7-4301-9a08-e8add6ab5697" xlink:to="loc_us-gaap_CommonStockSharesAuthorized_f5211732-bf62-49b5-ba19-39ccf10caec4" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesIssued_e3bbe232-fa09-4b56-8caf-5182ecb9c6d6" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockSharesIssued"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockLineItems_ae71f6dd-3ee7-4301-9a08-e8add6ab5697" xlink:to="loc_us-gaap_CommonStockSharesIssued_e3bbe232-fa09-4b56-8caf-5182ecb9c6d6" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding_35336d9a-1538-49d4-a579-a1fade563f90" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockSharesOutstanding"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockLineItems_ae71f6dd-3ee7-4301-9a08-e8add6ab5697" xlink:to="loc_us-gaap_CommonStockSharesOutstanding_35336d9a-1538-49d4-a579-a1fade563f90" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValue_c72c20ca-2031-409c-8d8b-c71d2f4b9922" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockLineItems_ae71f6dd-3ee7-4301-9a08-e8add6ab5697" xlink:to="loc_us-gaap_CommonStockValue_c72c20ca-2031-409c-8d8b-c71d2f4b9922" xlink:type="arc" order="4"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/ShareCapitalScheduleofCommonStockAuthorizedDetails" xlink:type="simple" xlink:href="hg-20240930.xsd#ShareCapitalScheduleofCommonStockAuthorizedDetails"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/ShareCapitalScheduleofCommonStockAuthorizedDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockLineItems_545937bd-5e8b-4933-9201-a124c8a66a4e" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ClassOfStockLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockByClassTable_583fd4ff-484c-4452-bcc4-8f25b6ebfbf1" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfStockByClassTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ClassOfStockLineItems_545937bd-5e8b-4933-9201-a124c8a66a4e" xlink:to="loc_us-gaap_ScheduleOfStockByClassTable_583fd4ff-484c-4452-bcc4-8f25b6ebfbf1" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementClassOfStockAxis_e4f9a3d0-ff45-483c-be27-952168898a68" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementClassOfStockAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfStockByClassTable_583fd4ff-484c-4452-bcc4-8f25b6ebfbf1" xlink:to="loc_us-gaap_StatementClassOfStockAxis_e4f9a3d0-ff45-483c-be27-952168898a68" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain_e4f9a3d0-ff45-483c-be27-952168898a68_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ClassOfStockDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_StatementClassOfStockAxis_e4f9a3d0-ff45-483c-be27-952168898a68" xlink:to="loc_us-gaap_ClassOfStockDomain_e4f9a3d0-ff45-483c-be27-952168898a68_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain_41529da8-baaf-48e3-a474-d7b36ab1d95f" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ClassOfStockDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_StatementClassOfStockAxis_e4f9a3d0-ff45-483c-be27-952168898a68" xlink:to="loc_us-gaap_ClassOfStockDomain_41529da8-baaf-48e3-a474-d7b36ab1d95f" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassAMember_82d744c2-3048-4e13-907f-6516ee3a4762" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonClassAMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockDomain_41529da8-baaf-48e3-a474-d7b36ab1d95f" xlink:to="loc_us-gaap_CommonClassAMember_82d744c2-3048-4e13-907f-6516ee3a4762" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassBMember_5fd32489-a8ca-401c-b5a6-e5b90b7da6a6" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonClassBMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockDomain_41529da8-baaf-48e3-a474-d7b36ab1d95f" xlink:to="loc_us-gaap_CommonClassBMember_5fd32489-a8ca-401c-b5a6-e5b90b7da6a6" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassCMember_2e46815f-7640-4055-a770-c768fb35dd52" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonClassCMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockDomain_41529da8-baaf-48e3-a474-d7b36ab1d95f" xlink:to="loc_us-gaap_CommonClassCMember_2e46815f-7640-4055-a770-c768fb35dd52" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_UnclassifiedCommonClassMember_2766a8a6-cc9f-48cc-a586-8dc1729ddab3" xlink:href="hg-20240930.xsd#hg_UnclassifiedCommonClassMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockDomain_41529da8-baaf-48e3-a474-d7b36ab1d95f" xlink:to="loc_hg_UnclassifiedCommonClassMember_2766a8a6-cc9f-48cc-a586-8dc1729ddab3" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_316dddf2-20f3-4ee4-8ffb-13e0eb46feca" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncreaseDecreaseInStockholdersEquityRollForward"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockLineItems_545937bd-5e8b-4933-9201-a124c8a66a4e" xlink:to="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_316dddf2-20f3-4ee4-8ffb-13e0eb46feca" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorized_e20ebeef-5741-419a-a99f-b75177747cd9" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockSharesAuthorized"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_316dddf2-20f3-4ee4-8ffb-13e0eb46feca" xlink:to="loc_us-gaap_CommonStockSharesAuthorized_e20ebeef-5741-419a-a99f-b75177747cd9" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_CommonStockSharesAuthorizedConversionOfConvertibleSecurities_3dadf589-a906-4234-81f9-dceecc5f4441" xlink:href="hg-20240930.xsd#hg_CommonStockSharesAuthorizedConversionOfConvertibleSecurities"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_316dddf2-20f3-4ee4-8ffb-13e0eb46feca" xlink:to="loc_hg_CommonStockSharesAuthorizedConversionOfConvertibleSecurities_3dadf589-a906-4234-81f9-dceecc5f4441" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_CommonStockSharesAuthorizedIncreaseDecrease_7a6735bd-6f3d-40e8-8b27-7e4d55f1ce6f" xlink:href="hg-20240930.xsd#hg_CommonStockSharesAuthorizedIncreaseDecrease"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_316dddf2-20f3-4ee4-8ffb-13e0eb46feca" xlink:to="loc_hg_CommonStockSharesAuthorizedIncreaseDecrease_7a6735bd-6f3d-40e8-8b27-7e4d55f1ce6f" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorized_3c65514a-0678-40a5-a5c5-c792bd598056" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockSharesAuthorized"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorized_f547ed39-1dd9-4276-97e0-1f0119b988a9" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockSharesAuthorized"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/ShareCapitalScheduleofCommonStockIssuedandOutstandingDetails" xlink:type="simple" xlink:href="hg-20240930.xsd#ShareCapitalScheduleofCommonStockIssuedandOutstandingDetails"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/ShareCapitalScheduleofCommonStockIssuedandOutstandingDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockLineItems_84b377a1-fb34-4e97-a4a3-b9228b81b8d9" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ClassOfStockLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockByClassTable_76e60d72-d35f-4201-b61c-99b7715a91dc" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfStockByClassTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ClassOfStockLineItems_84b377a1-fb34-4e97-a4a3-b9228b81b8d9" xlink:to="loc_us-gaap_ScheduleOfStockByClassTable_76e60d72-d35f-4201-b61c-99b7715a91dc" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementClassOfStockAxis_48db799a-d279-4097-99a5-59cc05860e61" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementClassOfStockAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfStockByClassTable_76e60d72-d35f-4201-b61c-99b7715a91dc" xlink:to="loc_us-gaap_StatementClassOfStockAxis_48db799a-d279-4097-99a5-59cc05860e61" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain_48db799a-d279-4097-99a5-59cc05860e61_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ClassOfStockDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_StatementClassOfStockAxis_48db799a-d279-4097-99a5-59cc05860e61" xlink:to="loc_us-gaap_ClassOfStockDomain_48db799a-d279-4097-99a5-59cc05860e61_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain_b3245090-3613-4431-bccc-a9ad2a435895" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ClassOfStockDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_StatementClassOfStockAxis_48db799a-d279-4097-99a5-59cc05860e61" xlink:to="loc_us-gaap_ClassOfStockDomain_b3245090-3613-4431-bccc-a9ad2a435895" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassAMember_b16c7ba7-e433-4797-9b02-c25f22cd0fa7" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonClassAMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockDomain_b3245090-3613-4431-bccc-a9ad2a435895" xlink:to="loc_us-gaap_CommonClassAMember_b16c7ba7-e433-4797-9b02-c25f22cd0fa7" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassBMember_67ca942a-02d5-48ad-95da-ca23815e86fc" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonClassBMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockDomain_b3245090-3613-4431-bccc-a9ad2a435895" xlink:to="loc_us-gaap_CommonClassBMember_67ca942a-02d5-48ad-95da-ca23815e86fc" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassCMember_369b90fb-4386-4b71-9439-2bb798dbda22" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonClassCMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockDomain_b3245090-3613-4431-bccc-a9ad2a435895" xlink:to="loc_us-gaap_CommonClassCMember_369b90fb-4386-4b71-9439-2bb798dbda22" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_cbf0789f-95c3-4ff4-9447-d68a7b9e3264" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncreaseDecreaseInStockholdersEquityRollForward"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockLineItems_84b377a1-fb34-4e97-a4a3-b9228b81b8d9" xlink:to="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_cbf0789f-95c3-4ff4-9447-d68a7b9e3264" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesIssued_8782d2c8-dafa-43cb-a3d4-085667607db2" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockSharesIssued"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_cbf0789f-95c3-4ff4-9447-d68a7b9e3264" xlink:to="loc_us-gaap_CommonStockSharesIssued_8782d2c8-dafa-43cb-a3d4-085667607db2" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding_c37bd27f-c8e0-4906-a377-8eb20eedd6f0" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockSharesOutstanding"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_cbf0789f-95c3-4ff4-9447-d68a7b9e3264" xlink:to="loc_us-gaap_CommonStockSharesOutstanding_c37bd27f-c8e0-4906-a377-8eb20eedd6f0" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_152ef528-aafa-4156-bbc1-c29173d0a820" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_cbf0789f-95c3-4ff4-9447-d68a7b9e3264" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_152ef528-aafa-4156-bbc1-c29173d0a820" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_ef7a99de-0bc6-4936-b5ac-0ec5aa2ed8a3" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_cbf0789f-95c3-4ff4-9447-d68a7b9e3264" xlink:to="loc_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_ef7a99de-0bc6-4936-b5ac-0ec5aa2ed8a3" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_9639f2d9-ef3d-4072-9724-67074178c924" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_cbf0789f-95c3-4ff4-9447-d68a7b9e3264" xlink:to="loc_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_9639f2d9-ef3d-4072-9724-67074178c924" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_14262117-adea-40a9-8f02-6a64c14bcab1" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_cbf0789f-95c3-4ff4-9447-d68a7b9e3264" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_14262117-adea-40a9-8f02-6a64c14bcab1" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchasedAndRetiredDuringPeriodShares_b82d8ead-b361-4d63-8c00-1b30921d07f0" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockRepurchasedAndRetiredDuringPeriodShares"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_cbf0789f-95c3-4ff4-9447-d68a7b9e3264" xlink:to="loc_us-gaap_StockRepurchasedAndRetiredDuringPeriodShares_b82d8ead-b361-4d63-8c00-1b30921d07f0" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesIssued_a8a5c1f4-edea-4f4c-9f13-c9f1a41cfb5d" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockSharesIssued"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding_a69036b6-ad4a-429c-a783-84bcd66b8282" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockSharesOutstanding"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/ShareCapitalNarrativeDetails" xlink:type="simple" xlink:href="hg-20240930.xsd#ShareCapitalNarrativeDetails"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/ShareCapitalNarrativeDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockLineItems_9d7e5822-c7f0-4291-892b-305965724dd4" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ClassOfStockLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockByClassTable_e2c8cd33-7efd-49e2-bab6-32ba26dd5c4e" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfStockByClassTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ClassOfStockLineItems_9d7e5822-c7f0-4291-892b-305965724dd4" xlink:to="loc_us-gaap_ScheduleOfStockByClassTable_e2c8cd33-7efd-49e2-bab6-32ba26dd5c4e" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementClassOfStockAxis_fee0c29c-bebe-4791-89f6-daf3c72b77fc" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementClassOfStockAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfStockByClassTable_e2c8cd33-7efd-49e2-bab6-32ba26dd5c4e" xlink:to="loc_us-gaap_StatementClassOfStockAxis_fee0c29c-bebe-4791-89f6-daf3c72b77fc" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain_fee0c29c-bebe-4791-89f6-daf3c72b77fc_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ClassOfStockDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_StatementClassOfStockAxis_fee0c29c-bebe-4791-89f6-daf3c72b77fc" xlink:to="loc_us-gaap_ClassOfStockDomain_fee0c29c-bebe-4791-89f6-daf3c72b77fc_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain_3ef23198-bbda-41b6-b1f4-4e545cd04358" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ClassOfStockDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_StatementClassOfStockAxis_fee0c29c-bebe-4791-89f6-daf3c72b77fc" xlink:to="loc_us-gaap_ClassOfStockDomain_3ef23198-bbda-41b6-b1f4-4e545cd04358" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassAMember_239d47d1-c494-469f-be67-14e0c001bc2e" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonClassAMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockDomain_3ef23198-bbda-41b6-b1f4-4e545cd04358" xlink:to="loc_us-gaap_CommonClassAMember_239d47d1-c494-469f-be67-14e0c001bc2e" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassBMember_c2c192f7-fc82-4b3a-9244-5d5f4f05b64b" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonClassBMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockDomain_3ef23198-bbda-41b6-b1f4-4e545cd04358" xlink:to="loc_us-gaap_CommonClassBMember_c2c192f7-fc82-4b3a-9244-5d5f4f05b64b" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassCMember_9c22d525-1352-47be-9e11-c0b5a2fe82ad" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonClassCMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockDomain_3ef23198-bbda-41b6-b1f4-4e545cd04358" xlink:to="loc_us-gaap_CommonClassCMember_9c22d525-1352-47be-9e11-c0b5a2fe82ad" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchasedAndRetiredDuringPeriodShares_1d2247e7-5a15-4f5a-8884-2e9e5afd8660" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockRepurchasedAndRetiredDuringPeriodShares"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockLineItems_9d7e5822-c7f0-4291-892b-305965724dd4" xlink:to="loc_us-gaap_StockRepurchasedAndRetiredDuringPeriodShares_1d2247e7-5a15-4f5a-8884-2e9e5afd8660" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockAcquiredAverageCostPerShare_9f5b7004-50d2-45c5-8bd7-abd23354ae14" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TreasuryStockAcquiredAverageCostPerShare"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockLineItems_9d7e5822-c7f0-4291-892b-305965724dd4" xlink:to="loc_us-gaap_TreasuryStockAcquiredAverageCostPerShare_9f5b7004-50d2-45c5-8bd7-abd23354ae14" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue_bec44805-36bc-49e6-bcbc-c0d0a493541d" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockRepurchasedAndRetiredDuringPeriodValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockLineItems_9d7e5822-c7f0-4291-892b-305965724dd4" xlink:to="loc_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue_bec44805-36bc-49e6-bcbc-c0d0a493541d" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StockRepurchaseProgramAuthorizedAmount1_d1da6be9-0629-4ef2-aa77-4bc00b4cff0e" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_StockRepurchaseProgramAuthorizedAmount1"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockLineItems_9d7e5822-c7f0-4291-892b-305965724dd4" xlink:to="loc_srt_StockRepurchaseProgramAuthorizedAmount1_d1da6be9-0629-4ef2-aa77-4bc00b4cff0e" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1_ca70df5b-6fa0-4d73-afa9-75e70b483db1" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockLineItems_9d7e5822-c7f0-4291-892b-305965724dd4" xlink:to="loc_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1_ca70df5b-6fa0-4d73-afa9-75e70b483db1" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_CommonStockVotingRightsClassAAndClassBLimitationAsAPercent_aa839f4e-f6cb-4e88-8bca-7406ef33d88f" xlink:href="hg-20240930.xsd#hg_CommonStockVotingRightsClassAAndClassBLimitationAsAPercent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockLineItems_9d7e5822-c7f0-4291-892b-305965724dd4" xlink:to="loc_hg_CommonStockVotingRightsClassAAndClassBLimitationAsAPercent_aa839f4e-f6cb-4e88-8bca-7406ef33d88f" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_518046c2-4ac1-4f09-a9a4-61c999f24581" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockLineItems_9d7e5822-c7f0-4291-892b-305965724dd4" xlink:to="loc_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_518046c2-4ac1-4f09-a9a4-61c999f24581" xlink:type="arc" order="6"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.hamiltongroup.com/role/SubsequentEventsNarrativeDetails" xlink:type="simple" xlink:href="hg-20240930.xsd#SubsequentEventsNarrativeDetails"/>
  <link:definitionLink xlink:role="http://www.hamiltongroup.com/role/SubsequentEventsNarrativeDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventLineItems_8ecaae8b-b69c-4def-87a7-1a42d6d83f48" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsequentEventLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTable_64ea674d-8e09-4caa-a439-4f57f187a431" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsequentEventTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_SubsequentEventLineItems_8ecaae8b-b69c-4def-87a7-1a42d6d83f48" xlink:to="loc_us-gaap_SubsequentEventTable_64ea674d-8e09-4caa-a439-4f57f187a431" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeAxis_54ab4f57-4f9e-4f0e-a0cb-cf83d5893bf3" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsequentEventTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_SubsequentEventTable_64ea674d-8e09-4caa-a439-4f57f187a431" xlink:to="loc_us-gaap_SubsequentEventTypeAxis_54ab4f57-4f9e-4f0e-a0cb-cf83d5893bf3" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeDomain_54ab4f57-4f9e-4f0e-a0cb-cf83d5893bf3_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsequentEventTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_SubsequentEventTypeAxis_54ab4f57-4f9e-4f0e-a0cb-cf83d5893bf3" xlink:to="loc_us-gaap_SubsequentEventTypeDomain_54ab4f57-4f9e-4f0e-a0cb-cf83d5893bf3_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeDomain_6dd40c62-fc69-4aa9-ad4d-5e1b1a0ff8fe" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsequentEventTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_SubsequentEventTypeAxis_54ab4f57-4f9e-4f0e-a0cb-cf83d5893bf3" xlink:to="loc_us-gaap_SubsequentEventTypeDomain_6dd40c62-fc69-4aa9-ad4d-5e1b1a0ff8fe" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventMember_e5dd3853-9d1e-420b-bb46-548f75119d08" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsequentEventMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SubsequentEventTypeDomain_6dd40c62-fc69-4aa9-ad4d-5e1b1a0ff8fe" xlink:to="loc_us-gaap_SubsequentEventMember_e5dd3853-9d1e-420b-bb46-548f75119d08" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis_8815acb0-0024-40b2-a352-7a991ce09d11" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_RangeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_SubsequentEventTable_64ea674d-8e09-4caa-a439-4f57f187a431" xlink:to="loc_srt_RangeAxis_8815acb0-0024-40b2-a352-7a991ce09d11" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember_8815acb0-0024-40b2-a352-7a991ce09d11_default" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_RangeMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_RangeAxis_8815acb0-0024-40b2-a352-7a991ce09d11" xlink:to="loc_srt_RangeMember_8815acb0-0024-40b2-a352-7a991ce09d11_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember_cd4d7d65-8f71-4730-8278-0201d1144294" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_RangeMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_RangeAxis_8815acb0-0024-40b2-a352-7a991ce09d11" xlink:to="loc_srt_RangeMember_cd4d7d65-8f71-4730-8278-0201d1144294" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MinimumMember_fa236c87-32f2-4d37-a6bb-566c9b9d0a4c" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_MinimumMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_RangeMember_cd4d7d65-8f71-4730-8278-0201d1144294" xlink:to="loc_srt_MinimumMember_fa236c87-32f2-4d37-a6bb-566c9b9d0a4c" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember_b817f478-855a-4ce1-a38f-c57d29c97989" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_MaximumMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_RangeMember_cd4d7d65-8f71-4730-8278-0201d1144294" xlink:to="loc_srt_MaximumMember_b817f478-855a-4ce1-a38f-c57d29c97989" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForCatastropheClaimsByCatastrophicEventAxis_7c9374a9-231e-45a5-8c44-e1eef92fe93d" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LiabilityForCatastropheClaimsByCatastrophicEventAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_SubsequentEventTable_64ea674d-8e09-4caa-a439-4f57f187a431" xlink:to="loc_us-gaap_LiabilityForCatastropheClaimsByCatastrophicEventAxis_7c9374a9-231e-45a5-8c44-e1eef92fe93d" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CatastrophicEventDomain_7c9374a9-231e-45a5-8c44-e1eef92fe93d_default" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CatastrophicEventDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_LiabilityForCatastropheClaimsByCatastrophicEventAxis_7c9374a9-231e-45a5-8c44-e1eef92fe93d" xlink:to="loc_us-gaap_CatastrophicEventDomain_7c9374a9-231e-45a5-8c44-e1eef92fe93d_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CatastrophicEventDomain_8009e432-68ce-45c6-878f-9458424a073f" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CatastrophicEventDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_LiabilityForCatastropheClaimsByCatastrophicEventAxis_7c9374a9-231e-45a5-8c44-e1eef92fe93d" xlink:to="loc_us-gaap_CatastrophicEventDomain_8009e432-68ce-45c6-878f-9458424a073f" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HurricaneMember_682f26cf-0f8b-45b2-8ebc-b48931d15fb7" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_HurricaneMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CatastrophicEventDomain_8009e432-68ce-45c6-878f-9458424a073f" xlink:to="loc_us-gaap_HurricaneMember_682f26cf-0f8b-45b2-8ebc-b48931d15fb7" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForCatastropheClaimsCarryingAmount_54dbf38d-39b8-439e-9dd7-77b0c04db5df" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LiabilityForCatastropheClaimsCarryingAmount"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SubsequentEventLineItems_8ecaae8b-b69c-4def-87a7-1a42d6d83f48" xlink:to="loc_us-gaap_LiabilityForCatastropheClaimsCarryingAmount_54dbf38d-39b8-439e-9dd7-77b0c04db5df" xlink:type="arc" order="0"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://xbrl.sec.gov/ecd/AwardTypeOnly" xlink:type="simple" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#AwardTypeOnly"/>
  <link:definitionLink xlink:role="http://xbrl.sec.gov/ecd/AwardTypeOnly" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_ValueAppreciationPoolMember_fd6b3317-1ac3-4aeb-ba22-380746f2c649" xlink:href="hg-20240930.xsd#hg_ValueAppreciationPoolMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:to="loc_hg_ValueAppreciationPoolMember_fd6b3317-1ac3-4aeb-ba22-380746f2c649" xlink:type="arc" order="3"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://xbrl.sec.gov/ecd/role/IndividualsOnly" xlink:type="simple" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#IndividualsOnly"/>
  <link:definitionLink xlink:role="http://xbrl.sec.gov/ecd/role/IndividualsOnly" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllIndividualsMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AllIndividualsMember"/>
    <link:loc xlink:type="locator" xlink:label="loc_hg_AlexBakerMember_9fd8919b-c9de-4a22-9b8c-7c57715ae132" xlink:href="hg-20240930.xsd#hg_AlexBakerMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_ecd_AllIndividualsMember" xlink:to="loc_hg_AlexBakerMember_9fd8919b-c9de-4a22-9b8c-7c57715ae132" xlink:type="arc" order="2"/>
  </link:definitionLink>
</link:linkbase>
