1) Bishopric 2) Diocese 3) Eparchy 
• (n.) The office or the province of an exarch.
Ex·ar'chate noun [ Late Latin exarchatus , from Latin exarchus : confer French exarchat .] The office or the province of an exarch. Jer. Taylor. 
Exarchate is a name of a province or territory under an exarch, or viceroy. In the 6th century Justinian formed the middle part of Italy into a province of the Eastern Empire, and gave the government of it to an exarch.
the office, jurisdiction, or province of an exarch.
An independent church within the Orthodox Church. The exarch, head of the exarchate, is an Eastern rite bishop who ranks below a patriarch and above a metropolitan.