i don't know about you but for me carry a bag with old "priority" tag is so embarassingly stroking that I wouldn't even think of doing it... in fact first thing I do when I pick up my luggage is to remove my tags (including priority tag)

and in answer to your question CX will graceously remove the old priority tag.

And to add to this: say if you had priority tag and you are entitled to new one, they will STILL remove the old tag and re-attach a brand new priority tag... i think that's waste of resources.