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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2022-01-09</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001566373</issuerCik>
        <issuerName>F-star Therapeutics, Inc.</issuerName>
        <issuerTradingSymbol>FSTX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001089409</rptOwnerCik>
            <rptOwnerName>DEPTULA-HICKS DARLENE M</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O F-STAR THERAPEUTICS, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>EDDEVA B920, BABRAHAM RESEARCH CAMPUS</rptOwnerStreet2>
            <rptOwnerCity>CAMBRIDGE</rptOwnerCity>
            <rptOwnerState>X0</rptOwnerState>
            <rptOwnerZipCode>CB22 3AT</rptOwnerZipCode>
            <rptOwnerStateDescription>UNITED KINGDOM</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Treasurer and CFO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>4.77</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2022-01-09</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>59823</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2032-01-09</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>59823</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>59823</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">These options were granted under the Issuer's 2019 Equity Incentive Plan.</footnote>
        <footnote id="F2">Twenty five percent (25%) of the total number of shares under the award shall vest on the first anniversary of the Vesting Commencement Date, January 9, 2022, and thereafter in 36 equal monthly installments such that the stock option shall be fully-vested on the fourth annual anniversary of the Vesting Commencement Date.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Darlene Deptula-Hicks</signatureName>
        <signatureDate>2022-01-11</signatureDate>
    </ownerSignature>
</ownershipDocument>
