Assuming that you are running this macro fro Outlook, you don't need to create a new Outlook instance. Use the active one.
You haven't told the macro what objItem is.
Assuming your paths are correct the following should work and I see nothing wrong with the line in question

Sub MoveDraftMail()

Dim objNamespace As Outlook.NameSpace
Dim objSourceFolder As Outlook.MAPIFolder
Dim objDestFolder As Outlook.MAPIFolder
Dim objItem As Object
Dim Archive_Folder As Outlook.MAPIFolder


    Set objNamespace = Application.GetNamespace("MAPI")
    Set objSourceFolder = objNamespace.folders(10).folders("HouseBillofLadingReport")
    Set Archive_Folder = objNamespace.folders("Online Archive - My@email").folders("Personal_Folders").folders("2021").folders("InBox")
    For Each objItem In objSourceFolder.items
        If TypeName(objItem) = "MailItem" Then
            objItem.Move Archive_Folder
        End If
        DoEvents
    Next objItem
    Set objDestFolder = Nothing
    Set objNamespace = Bothing
    Set objSourceFolder = Nothing
    Set Archive_Folder = Nothing
    Set objItem = Nothing
End Sub