Definitions of caliphate:

• noun:   the office of a caliph
• noun:   the territorial jurisdiction of a caliph
• noun:   the era of Islam's ascendaancy from the death of Mohammed until the 13th century; some Moslems still maintain that the Moslem world must always have a calif as head of the community

  Example: "Their goal was to reestablish the Caliphate"