The question is a good one and as everyone has pointed out, the answer is "wait and see". But the large elephant the large elephant in the room has a harp on its tail. I've no doubt reciprocity will be used to justify many policies and it will be very interesting to see what one gentleman does. He knows where his money comes from and he won't give up his UK (or will it be English by then?) revenue without a fight. Imagine having him on your side in a negotiation?
I'll stick my neck out and suggest that all the time we remain part of EASA licences will recognised and valid. What may change will be the future rights of those UK national not yet employed to work in the EU and vice-versa.