If an exhaust ability of a permanent is activated, and then that permanent leaves the battlefield and returns to the battlefield, it becomes a new object so its exhaust ability can be activated again.

You may activate this creature’s exhaust ability without discarding cards if you just want to put a +1/+1 counter on it.

Exhaust abilities can be activated any time you could normally activate an ability.

If an ability triggers whenever you activate an exhaust ability, that ability resolves before the exhaust ability resolves.