That's some string. I copied/pasted this into Access and put in various "& _" and added some quotes until I got no redlines. Here it is, hope it works for you.
Function Update()
On Error GoTo Update_Err
DoCmd.SetWarnings False
DoCmd.RunSQL "INSERT INTO tblArchive" & _
"( [Supplier ID], ContractTypeID, [Warranty Terms], [Ownership Terms], [Insurance Terms], " & _
"[Termination Terms], [Liability Terms], [Professional Indemnity Terms], [Intelectual Property Rights Terms], " & _
"[Disaster Recovery Terms], [Rates Terms], [Expenses Terms], [Nature of Agreement Terms], [Confidentiality Terms], " & _
"Definitions, [Export Lead Terms], [Delivarables Terms], [Support Terms], [Service Level Terms], [Response Times], " & _
"[Entire Agreement and Governing Law], ProjectTypeID, [Contract Start Date], [Contract End Date], [Link 1], [Link 2] ) " & _
"SELECT tblContractualAgreements.[Supplier ID], tblContractualAgreements.ContractTypeID, " & _
"tblContractualAgreements.[Warranty Terms] , tblContractualAgreements.[Ownership Terms], " & _
"tblContractualAgreements.[Insurance Terms], tblContractualAgreements.[Termination Terms], " & _
"tblContractualAgreements.[Liability Terms], tblContractualAgreements.[Professional Indemnity Terms], " & _
"tblContractualAgreements.[Intelectual Property Rights Terms], tblContractualAgreements.[Disaster Recovery Terms], " & _
"tblContractualAgreements.[Rates Terms], tblContractualAgreements.[Expenses Terms], " & _
"tblContractualAgreements.[Nature of Agreement Terms], tblContractualAgreements.[Confidentiality Terms], " & _
"tblContractualAgreements.Definitions, tblContractualAgreements.[Export Lead Terms], " & _
"tblContractualAgreements.[Delivarables Terms], tblContractualAgreements.[Support Terms], " & _
"tblContractualAgreements.[Service Level Terms], tblContractualAgreements.[Response Times], " & _
"tblContractualAgreements.[Entire Agreement and Governing Law], tblContractualAgreements.ProjectTypeID, " & _
"tblContractualAgreements.[Contract Start Date], tblContractualAgreements.[Contract End Date], " & _
"tblContractualAgreements.[Link 1], tblContractualAgreements.[Link 2]" & _
"FROM tblContractualAgreements WHERE (((tblContractualAgreements.[Contract End Date])=Date()));"
DoCmd.RunSQL "DELETE tblContractualAgreements.*, tblContractualAgreements.[Contract End Date]" & _
"FROM tblContractualAgreements WHERE (((tblContractualAgreements.[Contract End Date])=Date()));"
Update_Exit:
Exit Function
Update_Err:
MsgBox Error$
Resume Update_Exit
End Function