(1.) the title given, under the Byzantine emperors, to their viceroys in Italy and Africa, after Justinian's reconquest of those provinces.
(2.) The title was adopted in the early Church for the highest orders of the hierarchy. Primates or metropolitamas were styled ἔξαρχοι τῆς ἐπαρχίας, and the patriarchs were called ἔξαρχοι τῆς διοικήσεως. In the 6th canonm of Sardiea (A.D. 344) the former title (exarch of the eparchy) is given to primates; the third Council of Carthage, A.D. 397, forbade its use (Riddle, Antiquities, book 3, chapter 3). The exarch, as primate, was "inferior to the patriarch, and superior to the metropolitan. In the third century there were three exarchs, viz. Ephesus, with the diocese of Asia, 12 provinces and 300 sees; Heraclea, with the diocese of Thrace, and, 6 provinces, Caesarea, 13 provinces and 104 sees. The privileges of these exarchates were transferred by the Council of Chalcedon (A.D. 451) to the patriarch of Constantinople."
(3.) The exarch in the Greek Church at the present day is the patriarch's deputy, whose duty it is to visit the provinces under, his inspection, to inform himself as to the lives and morals of the clergy; to take cognizance of eclesiastical causes — the manner of celebrating divine ordinances, the sacraments, particularly confession, the observance of the canons, monastic discipline, affairs of marriages, divorces, etc.; but, above all, to take account of the revenues which the patriarch receives from the several churches. — Bingham, Orig. Eccles. Bohn's ed. 1:61, 67.