banisher priest exile

[DirtyMustachio]

Say I {banisher priest} and choose to exile a {mistcutter hydra}

Do counters resume to stay on creature if banisher leaves play

[Pleeb]

They cease to exist the moment the hydra leaves the battlefield, so no, they do not.

121.2.: Counters on an object are not retained if that object moves from one zone to another. The counters are not "removed"; they simply cease to exist. See rule 400.7.