Priest has risen in power significantly and I feel that the ideal build has only been realized by few duels players so far. Joras Thuldoom, the new Priest Treasure, is absolutely insane and wins games on its own. 

The deck has 3 win conditions that you can use to win:

Joras Thuldoom: The deck is tailored to draw Joras and get at least 4 of them by as early as turn 4. Raise dead also has a large probability of getting more Joras'. Grimmer patron is a huge pickup as a treasure if you are offered it, because if your opponent is ever missing removal just once, you've won the game.

C'thun: The deck cycles very quickly through itself as a result of your hero power, so if you aren't able to kill your opponent with Joras, C'thun should be able to consistently hit the board, especially in earlier matches.

Anti--Aggro: In aggro matchups, cards like radiance, priest of the feast, and even your own hero power make this deck easy to outvalue and survive through aggressive opponents.

Cards to switch out:

Nazmani bloodweaver is most likely your first cut if you want to run something else in it's place.

Enjoy the deck and let me know your experiences and thoughts on what you would change from the list!

Update: Swapping out draconic studies and Nazmani bloodweaver for Wild Pyromancer and Thoughtsteal, Nazmani is definitely not worth it in this build.