Time machine does not work on my new MACBook Pro following migration from old MAC

Although I can't say this for certain, I think the Time Machine backup is "tied" to your old Mac...hence, your new one can't use it.

You'll want to erase/reformat the external drive with your new Mac. (Might even rename it to remind yourself which computer it's tied to). Here's an Apple Support article that spells out how to do this: Erase and reformat a storage device in Disk Utility on Mac - Apple Support

MacMikeinOK is right that the drive belongs to the old Computer. Time Machine backup up your Computer, not just one user.

But you should be able to "Inherit" the old backup drive when you start Time Machine on the new Mac with the drive attached. if not, try holding the Option button while you clink on the Time Machine icon on the menubar, and choose 'browse other backup disks'.