government over an ethnic group
• (n.) The dominion of an ethnarch; principality and rule.
Eth'narch·y noun [ Greek ....] The dominion of an ethnarch; principality and rule. Wright. 
ethnarchy 1. The dignity or office of an ethnarch. 2. The dominion of, or province ruled by, an ethnarch (a ruler of a province of people). 3. Government over or rule of an ethnic group
the government, office, or jurisdiction of an ethnarch.