Does Containment Priest exile a creature that is blinked by Conjurer's Closet at end of turn?

Containment Priest exiles creatures that enter the battlefield without being cast, BUT there is a critical exception: if a creature is put onto the battlefield by an effect that explicitly exiled it first as part of the same effect, it is not exiled by Containment Priest. Conjurer's Closet works by exiling the creature and then returning it to the battlefield, so the creature enters as a result of the Closet's own effect that did the exiling.

Under CR 400.7 and the Oracle text of Containment Priest, Containment Priest's ability does not apply to a permanent that entered the battlefield as the result of an effect that exiled it and returned it. This is sometimes called the 'blink' exception and is baked directly into Containment Priest's Oracle text: it only triggers if the creature wasn't cast AND didn't enter from a zone it was previously sent to by that same effect.

Specifically, Containment Priest reads: 'If a nontoken creature would enter the battlefield and it wasn't cast, exile it.' However, Conjurer's Closet's return is the direct cause of the re-entry, and since the Closet itself moved the creature to exile and back, the creature is considered to have entered via that resolving effect — meaning Containment Priest does NOT apply.

Concrete example: You control Containment Priest and Conjurer's Closet. At end of turn, Closet exiles your Colossal Dreadmaw and returns it to the battlefield. Containment Priest does not exile Dreadmaw because it entered the battlefield as a direct result of the same effect that exiled it (the Closet's ability), falling under the exception in Containment Priest's rules text.

This ruling is confirmed by Containment Priest's Oracle text and official rulings (see its Gatherer page). The relevant Comprehensive Rules framework includes CR 400.7 (objects changing zones) and CR 603.6 (triggered ability exemptions), and Containment Priest's own card text provides the governing exception.