Archbishop is a title held by a Sabbatvampire who has claimed a given expanse of domain as his own, generally a city, and supports that claim against all others. The term can refer to a Cainite of either sex.
With many of the same powers as a CamarillaPrince, the Archbishop is the closest analog the Sabbat has to that position. An Archbishop is different, though, in that the Sabbat is less concerned with enforcing the Traditions and more concerned with waging its holy war against the Antediluvians and everyone else. Thus, the Archbishop is part spiritual leader and part warlord, advancing the Sword of Caine’s agenda and establishing Cainite primacy.
This last is a difficult task to undertake, as it’s not simply a question of turning a Sabbat city into a living hell and declaring that vampires rule; the fundamentals of the Masquerade and the sheer weight of the mortal population means that is a war to be waged in stages. Too many Sabbat fail to understand this, especially among the young, and lose faith in their leadership because they’re too impatient to play out the long-game Jyhad. This subversion of ignorance is perhaps the Archbishop’s greatest challenge to overcome.
The Archbishops usually are the highest rank in a city hierarchy, served by bishops and Templars, but answering directly to the Cardinals, who coordinate them in their cities and direct them in the Jyhad. They serve their territory's Cardinal holding sway over a smaller region.
Such vampires usually rise through the ranks, serving lengthy tenures as priests or bishops of the sect. Each Cardinal has the power to appoint whomever he wishes to the position of Archbishop. Some accept bribes, but vampires who gain their positions in this manner often have difficulty to remain in office for long before Final Death catches up to them. Multiple Archbishops preside over these smaller domains, all contained within a single Cardinal's region.