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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2023-03-13</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001969365</rptOwnerCik>
            <rptOwnerName>Pimblett Emily</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>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Accounting Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>6.10</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2031-04-26</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>35000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>8.21</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2032-01-26</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>30000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>3.27</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <value>2032-10-30</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>30000</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 26, 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 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 in equal monthly installments, at a rate of 1/48th of the total number of shares on each monthly anniversary of January 27, 2022 (the &quot;January 2022 Vesting Commencement Date&quot;) 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 January 2022 Vesting Commencement Date.</footnote>
        <footnote id="F3">The shares subject to this option shall vest in equal monthly installments, at a rate of 1/48th of the total number of shares on each monthly anniversary of October 31, 2022 (the &quot;October 2022 Vesting Commencement Date&quot;) 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 October 2022 Vesting Commencement Date.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Brian Woodard, Attorney-in-Fact</signatureName>
        <signatureDate>2023-03-21</signatureDate>
    </ownerSignature>
</ownershipDocument>
