I would not attempt to make such a transition. I would work with the old T and make sure there was no open wound or infection before I moved on. It does not sound like you were ready to quit with this T.

I can see transition if the old T is handing you off to a new T, then both T's help you with that but if you have decided not to see an old T, that's like deciding not to see any other professional (your old accountant or lawyer) and you just work with the new on whatever issues you have right now. If you have not finished with your old T though, you may have trouble with a new T as you will be out of sync and working on old T problems without old T.