First of all welcome to TBL!
Secondly, I think the answer may be... kind of?
In that if you wanted the begin as GM at another level, retaining your previous GM points and for example wanted to take on an NHL team you might have the reputation to pull it off given you have 20 years experience...
You'd have to retire from your job with the Olympiques but not "Retire from hockey" leaving you active but unemployed. You'd then have to wait until you can find a job opening to be appointed to... I think the only news items you'll get are when jobs turn over...
I don't know the exact mechanics of that because I've never moved leagues; but someone who has may be able to help you out with the details.
Otherwise yeah you'd have to add a new GM to take your pick of where you'd like to go next and you'd start with zero rep again.