Say I {banisher priest} and choose to exile a {mistcutter hydra}
Do counters resume to stay on creature if banisher leaves play
They cease to exist the moment the hydra leaves the battlefield, so no, they do not.
121.2. (http://imtgapp.com/forum/index.php?action=imtg;area=rule;number=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.