Priest is always a weird class in arena. It's probably teir 3 right now. Having said that, if I could I delete that stupid class from the game. The problem with priest is it's usually pretty in consistent to get a good deck and it has a pretty specific play style. But if it is working it is the most ungodly bullshit that ever happens in the game. Things like shadow madness, northshire cleric, mind control, and "let me change your mind" are just infuriating. And that's just the classic set. Add drakonid operator, cabal talon priest, potion of madness etc and the bullshit just gets infinitely worse.
TLDR priest is not a "good" class but if it gets it's broken cards it can be the worst experience ever for the opponent cuz bullshit priest things.