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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2021-08-09</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001768446</issuerCik>
        <issuerName>Eliem Therapeutics, Inc.</issuerName>
        <issuerTradingSymbol>ELYM</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001233539</rptOwnerCik>
            <rptOwnerName>PATTERSON LEONE D</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O ELIEM THERAPEUTICS, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>23515 NE NOVELTY HILL RD, STE. B221 #125</rptOwnerStreet2>
            <rptOwnerCity>REDMOND</rptOwnerCity>
            <rptOwnerState>WA</rptOwnerState>
            <rptOwnerZipCode>98053</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>1.32</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2031-03-05</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>39198</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>6.10</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2031-04-26</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>15383</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The shares subject to this option shall vest at a rate of 12/48ths of the total number of shares on the one-year anniversary of March 4, 2021 (the &quot;March 2021 Vesting Commencement Date&quot;) and 1/48th of the total number of shares each monthly anniversary of the March 2021 Vesting Commencement Date thereafter (or if there is no corresponding day, on the last day of the month) for so long as the Reporting Person remains an officer, director, employee, consultant and/or advisor of the Issuer, such that the total number of shares shall be fully vested on the four-year anniversary of the March 2021 Vesting Commencement Date.</footnote>
        <footnote id="F2">The shares subject to this option shall vest at a rate of 12/48ths of the total number of shares on the one-year anniversary of April 27, 2021 (the &quot;April 2021 Vesting Commencement Date&quot;) and 1/48th of the total number of shares each monthly anniversary of the April 2021 Vesting Commencement Date thereafter (or if there is no corresponding day, on the last day of the month) for so long as the Reporting Person remains an officer, director, employee, consultant and/or advisor of the Issuer, such that the total number of shares shall be fully vested on the four-year anniversary of the April 2021 Vesting Commencement Date.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Alan Hambelton, Attorney-in-Fact</signatureName>
        <signatureDate>2021-08-09</signatureDate>
    </ownerSignature>
</ownershipDocument>
