Well there will be spoilers in some regards here so if you don't want to hear them don't read this and then complain I wrote them.
So if you haven't heard yet they are putting in the events of the book Twilight of the Aspects concerning the Archbishop. In the new instance Hour of Twilight Archbishop Benedictus is the final encounter in the Wyrmrest Temple. So totally ignoring the fact that the world could end let's talk about how the church will recover from losing its figure head.
Will the church itself fall apart? I really doubt it. The light in Warcraft is so ingrained in the way things work the church itself is safe even if its highest ranking member has decided to forsake his own teachings and serve the being that wants the world to end and everyone within it to die horrible deaths. Then what is to become of it?
Who will lead it? Well there has been some talk that Anduin Wyrnn Prince of Stormwind would be a great choice. The light within him is seen as very strong. In Wolfheart, Velen himself seen by many people as a Jesus archetype says the light is very strong in him more then anyone else he has ever come in contact with. Now remember that Velen himself has been in direct contact with a few Nauru beings of pure light, and he is able to say this about Anduin.
Now I believe Anduin himself will be one of the most interesting characters in Warcraft, but he is only 13 years old. I don't think he will be the head of the Church this soon because logically will the other bishops choose to follow him because of how the light runs within him or because he is their future king? With this being an issue I don't think it can happen when he is this young. So then what? Well I just see someone in as a placeholder until Anduin can take the spot which will be rightfully his. In regards to when this will take place, well I believe Anduin will play a major role when we are dealing with Demons and Argus.