An Exarchate is any territorial jurisdiction (secular or ecclesiastical) whose ruler is described as an exarch.
Administration of the secular Byzantine Empire
Apostolic exarchates in the Eastern Catholic churches
Maronite Catholic Patriarchal exarchates
Melkite Greek Catholic Patriarchal exarchates
Ukrainian Catholic Archiepiscopal exarchates
Exarchates of the Ecumenical Patriarchate of Constantinople