Been thinking about if a Witch Hunter can become a Priest.

One of my players play a Witch Hunter (careers Zealot, Flagelant, Prophet of Doom, Witch Hunter, Witch Hunter Captain), could this character advance into Initiate (of Sigmar) after completing the last career in this? I never read anything about a Witch Hunter becoming a Priest (or the other way around), but they are all devoute Sigmarites, so it could be fitting.

What do you all think?

I don't see any problem in rules.  Narratively, becoming a priest is supposed to take time.  If you played that Witch Hunters are in fact Templars of Sigmar, this might be cut down.

Well, as long as it fits your story, I don't see much of a problem with it. I agree with valvorik that it would be especially "easy" to become an Initiate of Sigmar.

One thing for the player to keep in mind, however, is the "influence" loss. A Witchhunter Captain is a position of authority, respected in both secular and religious (well Sigmarite) circles. A simple priest won't have much authority of a Witchhunter Captain.  An Initiate is nearly the bottom of the barrel of the religious order. Any priest in the order (and some not in the same order) will have authority over the Initiate. It is, in a sense, a demotion in "rank" (not talking about XP rank).  So, keep in mind therefore that such a career change should be represented by the character having a strong sense of "religious calling".  He was already serving Sigmar in a powerful capacity as a witchhunter captain. So, what has motivated the character to enter into the religious order itself, and putting up with being a novice as well?

Really, as a GM, that is the question I would pose to the player. I'm sure that story-wise the higher members of the order itself would want to know the answer before they admitted the character into their ranks. I don't have a technical difficulties with the transition (Honestly, I'd probably have more with leaving the priesthood once it has been entered, than joining).