Loki, it depends on what the new manager is given to work with.
Rafa had 2 battles to fight, the football competitions, and the H&G owners (lcak of control, only allowed to buy mediocre players, with the exception of Torres, etc).
I hope that FSG is smart enough to learn from recent mistakes. The new manager needs to present a sensible plan to FSG, and if approved, then he needs to have complete freedom of operation. No Damians in the way, no loyalties to anyone but to the club.
FSG will set objectives depending on what resources are given to the new manager. There will be short and long term objectives, that's the way businesses operate. If short term goals are not achieved, then I expect FSG to take corrective action, depending on how the evaluation goes.