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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2021-06-08</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001458891</issuerCik>
        <issuerName>Noble Corp</issuerName>
        <issuerTradingSymbol>NE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001163368</rptOwnerCik>
            <rptOwnerName>PACIFIC INVESTMENT MANAGEMENT CO LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>650 NEWPORT CENTER DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEWPORT BEACH</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>92660</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Ordinary Shares</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>26709221</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Warrants (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>19.27</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2021-02-05</value>
            </exerciseDate>
            <expirationDate>
                <value>2028-02-04</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Ordinary Shares</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>312913</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Warrants (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>23.13</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2021-02-05</value>
            </exerciseDate>
            <expirationDate>
                <value>2028-02-04</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Ordinary Shares</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>312913</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The securities reported in the table above are held by certain funds and accounts for which the Reporting Person serves as investment manager, advisor or sub-advisor, including the PIMCO Global Credit Opportunity Fund, which holds 8,849,999 ordinary shares, warrants to purchase 310,269 ordinary shares with an exercise price of $19.27 per share and warrants to purchase 310,269 ordinary shares with an exercise price of $23.13 per share. The Reporting Person disclaims beneficial ownership in the reported securities, except to the extent of its pecuniary interest therein.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Jason Nagler, Senior Vice President, Pacific Investment Management Company LLC</signatureName>
        <signatureDate>2021-06-08</signatureDate>
    </ownerSignature>
</ownershipDocument>
