<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>5</documentType>

    <periodOfReport>2022-12-31</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <form3HoldingsReported>0</form3HoldingsReported>

    <form4TransactionsReported>0</form4TransactionsReported>

    <issuer>
        <issuerCik>0001859285</issuerCik>
        <issuerName>HireRight Holdings Corp</issuerName>
        <issuerTradingSymbol>HRT</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001889191</rptOwnerCik>
            <rptOwnerName>RJC GIS Holdings LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O HIRERIGHT HOLDINGS CORPORATION,</rptOwnerStreet1>
            <rptOwnerStreet2>100 CENTERVIEW DRIVE, SUITE 300</rptOwnerStreet2>
            <rptOwnerCity>NASHVILLE</rptOwnerCity>
            <rptOwnerState>TN</rptOwnerState>
            <rptOwnerZipCode>37214</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001888105</rptOwnerCik>
            <rptOwnerName>Conrad Jeanne S.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O HIRERIGHT HOLDINGS CORPORATION,</rptOwnerStreet1>
            <rptOwnerStreet2>100 CENTERVIEW DRIVE, SUITE 300</rptOwnerStreet2>
            <rptOwnerCity>NASHVILLE</rptOwnerCity>
            <rptOwnerState>TN</rptOwnerState>
            <rptOwnerZipCode>37214</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001889222</rptOwnerCik>
            <rptOwnerName>Conrad Raymond W.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O HIRERIGHT HOLDINGS CORPORATION,</rptOwnerStreet1>
            <rptOwnerStreet2>100 CENTERVIEW DRIVE, SUITE 300</rptOwnerStreet2>
            <rptOwnerCity>NASHVILLE</rptOwnerCity>
            <rptOwnerState>TN</rptOwnerState>
            <rptOwnerZipCode>37214</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2022-12-22</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>5</transactionFormType>
                <transactionCode>G</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>125000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>10770969</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">All of the interests in RJC GIS Holdings, LLC are held by (a) The Raymond W. Conrad Revocable Trust dated April 17, 2009, of which Raymond Conrad is trustee; (b) The Jeanne S. Conrad Revocable Trust dated April 17, 2009, of which Jeanne Conrad is trustee; (c) The RWC Family Trust, of which Jeanne Conrad is trustee; and (d) the JSC Family Trust, of which Raymond Conrad is trustee.</footnote>
        <footnote id="F2">The reporting persons state that neither the filing of this statement nor anything herein shall be deemed an admission that such person is, for purposes of Section 16 of the Securities Exchange Act of 1934, as amended (the &quot;Exchange Act&quot;), or otherwise, the beneficial owner of any securities covered by this statement. The reporting persons disclaim beneficial ownership of the securities covered by this statement, except to the extent of the pecuniary interest of such person in such securities.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>RJC GIS HOLDINGS, LLC By: /s/ Raymond W. Conrad Name: 	Raymond W. Conrad Title: President</signatureName>
        <signatureDate>2023-02-06</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>JEANNE S. CONRAD By: /s/ Jeanne S. Conrad</signatureName>
        <signatureDate>2023-02-06</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>RAYMOND W. CONRAD By: /s/ Raymond W. Conrad</signatureName>
        <signatureDate>2023-02-06</signatureDate>
    </ownerSignature>
</ownershipDocument>
