Does a creature with persist that returns from the graveyard trigger enter-the-battlefield effects?

Persist (CR 702.79) is a triggered ability that triggers when the creature dies with no -1/-1 counters on it. It then returns that creature card to the battlefield from the graveyard under its owner's control with a -1/-1 counter on it. Crucially, this return is a brand-new event of the permanent entering the battlefield.

Under CR 614.12 and the general rules governing triggered abilities (CR 603.2), any time a permanent enters the battlefield, all 'enters the battlefield' triggers from any source on the battlefield — including the returning creature's own abilities — are evaluated and queued to trigger. The persist ability itself does not suppress these triggers in any way.

It is also important to note that, per CR 400.7, the card returning via persist is treated as a new object with no memory of its previous existence on the battlefield. This means it loses any auras or equipment it had before dying, but it also means it freshly qualifies as 'entering the battlefield' for every ETB trigger.

Concrete example: You control a Reveillark and a Woodfall Primus (which has persist and an ETB trigger that destroys a noncreature permanent). Woodfall Primus dies with no -1/-1 counters. Persist triggers, returning it to the battlefield — as it enters, its ETB trigger fires again, allowing you to destroy another noncreature permanent.

So yes: every ETB effect — whether it's on the returning creature itself, on other permanents, or from replacement effects — applies fully when a persist creature re-enters the battlefield.