Repeating the process includes the instruction to repeat the process. That is, you’ll keep exiling cards and putting them onto the battlefield until you fail to put a permanent card onto the battlefield.

If putting any of those permanent cards onto the battlefield causes abilities to trigger, those abilities will wait to go on the stack until Primal Surge has finished resolving. Starting with the active player, each player puts their abilities on the stack in any order.

If you exile a permanent card that you can’t put onto the battlefield (such as an Aura with nothing legal to enchant) or one you don’t want to put onto the battlefield, Primal Surge finishes resolving.

A permanent card is an artifact, creature, enchantment, land, or planeswalker card.