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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2021-10-27</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001283140</issuerCik>
        <issuerName>HOLLY ENERGY PARTNERS LP</issuerName>
        <issuerTradingSymbol>HEP</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001602297</rptOwnerCik>
            <rptOwnerName>Norwood Kenneth</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2828 N. HARWOOD</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 1300</rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75201</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>VP and Controller</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Units</value>
            </securityTitle>
            <transactionDate>
                <value>2021-10-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>4845</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>61928</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Phantom Units granted under the Holly Energy Partners, L.P. Long-Term Incentive Plan.  The phantom units vest in three equal annual installments beginning December 1, 2022, provided that the reporting person remains in the employ of the Issuer from the grant date through each such vesting date.  The vested phantom units will be paid within 30 days following the vesting date in the form of the Issuer's common units equal to the number of vested phantom units.</footnote>
    </footnotes>

    <remarks>Mr. Norwood is Vice President and Controller of Holly Logistic Services, L.L.C. Holly Logistic Services, L.L.C. is the general partner of HEP Logistics Holdings, L.P., the general partner of Issuer.</remarks>

    <ownerSignature>
        <signatureName>Stacey Foland, Attorney-in-Fact</signatureName>
        <signatureDate>2021-10-29</signatureDate>
    </ownerSignature>
</ownershipDocument>
