Priory asks the group to make deliberate stop assignments. Pull control matters because several enemy casts heal, enrage, or interrupt the whole party.
First area: remove Captain Dailcry's protection first: Kill the three mini-bosses before Captain Dailcry so Strength in Numbers is removed. On the way, stop Arathi Footmen's Defend, Devout Priests' Greater Heal, and Fanatical Conjurors' Fireball while staying out of Caltrops and Flamestrike.
Captain Dailcry: frontal, enrage, and targeted defensive: Sidestep Earthshattering Spear, interrupt Battle Cry, and use a personal if Savage Mauling targets you. The tank should actively mitigate Pierce Armor rather than trying to heal through stacks.
Prioress Murrpray: execute the shield transition: Face away for Blinding Light, keep moving with The Sacred Flame, then break Barrier of Light and interrupt Embrace the Light. Save the major healing cooldown for Inner Fire, not for incidental damage just before it.
These are execution priorities, not a fixed pull-count route. Verify weekly tuning, affixes, and your tank's route before the key, then use the source and current videos for difficulty-specific details.
Call the safe side before the cast and keep the group out of Consecration. That preserves a stable melee stack and prevents the encounter from drifting across the room.