Laserbeak will perch on anyone's shoulder if they're scary enough.
As for a successor, we already know the answer to this one: Razorclaw.
Razorclaw refused to accept the terms of the Pax Cybertronia, and went rogue. He forged a new group of Predacons and led them, with the intention of taking their rightful place as the rulers of Cybertron. He survived an assassination attempt by the Tripredacus Council and continues to quietly manipulate events, at least up until the events of the Beast Wars
Razorclaw could've laid down his arms. He might've been granted amnesty at the war's conclusion. Instead, he chose to pursue his rightful destiny of galactic conquest, as a Con should.
Rejecting the established order and striking out on one's own, even if it means war, is always how Megatron began. It is also how the founder of the Predacons reacted to the strict demands of new Autobot rule.
Hail Razorclaw, the founder of the Predacons and new Emperor of Destruction!