Apostolate

Charles Buck Theological Dictionary

In a general sense, is used for mission; but it more properly denotes the dignity or office of an apostle of Christ. It is also used in ancient writers for the office of a bishop. But as the title apostolicus has been appropriated to the pope, so that of apostolate became at length restrained to the sole dignity of the popedom.

Webster's Dictionary

(1): (n.) The dignity, office, or mission, of an apostle; apostleship.

(2): (n.) The dignity or office of the pope, as the holder of the apostolic see.