Holy Priest/Warrior Arena Matchups Guide by Darkalpha

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You have the advantage here, but if they get some mana burns off on you they can win.
Your warrior will sit on their priest, this will prevent mana burns on you, but it will also force their warrior to either go on you, or sit on your warrior and feed him rage. (when he isn’t being rooted or cyclone, which should be for 90% of the fight.)
The warriors will charge each other, when they do, get to max range, faerie fire their warrior(more dps) and lifebloom yours. As soon as your warrior can, he needs to intercept the priest and get on him. Their warrior will then either turn to you, or go after your warrior.

If he sticks on your warrior(Most will):
This is tricky because you need to make sure you’re always as far away as you can to be able to LOS burns, but making sure that you’re always in LOS to heal your warrior. You need to keep a very close on the priest, like always, to make sure he isn’t dispelling your warrior’s hots. Do your best to make sure the other warrior is on lockdown, cycloning/rooting him nonstop to give your warrior as much time alone with the priest as possible. If the Priest is dispelling your warrior, it’s costing him mana, but if your warrior ever gets to around 50%, he needs to shield up until you bring him back to full, because a chastise->fear(from either either priest or warrior) combo can sometimes give them enough time to finish off your warrior. Because the warrior is on your warrior, you should be able to CC him easily, but be mindful of the priest to prevent eating a mana burn. (/wave pwyff <3) Eventually, the priest will go oom from staying alive, then you can finish them off.

If he goes to you(very rare)
Survive. The Warrior will not be able to kill you before your warrior kills their priest. You should have no trouble escaping a warrior, but if he gets really lucky with stuns and gets your low, a timely intercept/intervene +disarm from your warrior will save you. You likely won’t be able to CC him as much, but since the warrior will be on the other side of a pillar from you, he's being controlled just as well as if he was rooted/cycloned.

Notes:
-Rank 1 MF/Faerie Fire on the rooted warrior to give your roots dispel fodder that the priest has to dispel through.
Do your best to stay far away and next to a pillar to give yourself both LOS breaking and your warrior an escape option via intervene.