Typically not. We might have temporary assignments, or a measure of authority granted by special circumstances -- sometimes you've got to negotiate something in the field to stop a conflict, or you might need to serve as a representative at a conference. But for the most part, we serve the government, and we won't keep a position in it while our Starfleet commissions are active.

[But then, Starfleet tends to attract people who'd chafe at being tied down to a desk. Who really wants to give up flying around?]

It's hard to govern if you and your ship have to be moving on to the next sector next week.