Sunni Islam is not at all like the medieval Catholic church, and so I give you the:
Organization of the Islamic Faith
The Caliph - The Caliph sits as the greatest scholar and priest in all of the lands. A descendant of the Caliphs of Baghdad, the Caliph is a hereditary position, and should a line completely die out, then the greatest of all scholars in the lands, the ulamas, must gather to select the next closest line. In practice, the Caliph's powers are rather limited, since he leads a pack of absolute monarchs, many of whom are very strong-willed.
The ulamas - The ulamas are great scholars, with enormous influence in their own realms. When the Caliph desires council from other mortal men, then he summons these wisemen to a conclave. Generally, he will call a Conclave before he declares a ruler apostate, or calls a jihad, although there have been exceptions for flagrant cases. Should a Caliph die without issue, then it falls to the ulamas to divine who is to succeed him. Each Sunni muslim nation has one ulama. Also, the holiest of cities, with their great circles of clerical scholars also recieve an ulama. Those cities are:
Mecca
Medina
Astrakhan
Jerusalem
Note: Baghdad is not among the holy cities since Timur killed everyone in it, and the great scholars have gone to reside in Astrakhan with the Caliph. So, should it come up, every Sunni nation will get one ulama, except for the Hedjaz, which has three, the Golden Horde, which has two, and Austria will also recieve one, since they control Jerusalem.
