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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2021-03-01</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001819253</issuerCik>
        <issuerName>Haymaker Acquisition Corp. III</issuerName>
        <issuerTradingSymbol>HYACU</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001161492</rptOwnerCik>
            <rptOwnerName>HEYER STEVEN J</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>501 MADISON AVENUE, FLOOR 12</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10022</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>See Remarks</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Class B Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>8625000</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">As described in the issuer's registration statement on Form S-1 (File No. 333-253010) under the heading &quot;Description of Securities--Founder Shares&quot;, the shares of Class B common stock will automatically convert into shares of Class A common stock at the time of the issuer's initial business combination, on a one-for-one basis, subject to certain adjustments described therein and have no expiration date.</footnote>
        <footnote id="F2">These shares represent Class B common stock held by Haymaker Sponsor III LLC (the &quot;Sponsor&quot;) acquired pursuant to a subscription agreement by and between the Sponsor and the issuer. The Class B common stock owned by the Sponsor includes up to 1,250,000 shares that are subject to forfeiture in the event the underwriters of the issuer's initial public offering do not exercise in full their over-allotment option as described in the issuer's registration statement.</footnote>
        <footnote id="F3">Steven J. Heyer is the Chief Executive Officer and Director of the issuer, and is a managing member of the Sponsor.  He has voting and investment discretion with respect to the securities held by the Sponsor. As such, Mr. Heyer may be deemed to share beneficial ownership of the shares of Class B common stock held directly by the Sponsor. Mr. Heyer disclaims any beneficial ownership of the reported shares other than to the extent of any pecuniary interest he may have therein, directly or indirectly.</footnote>
    </footnotes>

    <remarks>Chief Executive Officer and Director</remarks>

    <ownerSignature>
        <signatureName>/s/ Steven J. Heyer</signatureName>
        <signatureDate>2021-03-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
