Priests can be very difficult depending on their
Priest: Priests can be very difficult depending on their Anarchy credits build. Holy and Discipline Priest are a regular endurance game, but Shadow Priests are very hard because of their added DPS.
Trying to outlast a priest is nearly impossible since they have a much higher mana pool and more potent heals, so it is often best to try and blast them down as carefully as possible. Their main tactic will be to try and burn down all of your mana with their Mana Burn abilities.
Your best option against this is to simply use all of your mana up instead trying to take them down with Holy Shock and mass Judgments. Their second best ability is their instant Fear, which gives them time to heal back up.
Your only hope is to try and resist it or use your PVP trinket to break out of it. They will try and use it every thirty seconds so if you can keep track of the time you can plan for when it may happen and not waste your abilities or seals.
Fortunately this is their only real way to interrupt your healing. If you are ever low on health you can heal yourself with little worry about being stunned or interrupted.
When you can stun them with your Hammer of Justice when you see them casting spells and judge them for Command whenever possible, Regardless of their build they will be doing most of their damage with shadow based attacks.