Yours, Etc.: Origins and Uses of 8 Sign-Offs
late Old English tetrarche "ruler of one of four divisions of a kingdom or province," from Late Latin tetrarcha, from Greek tetrarkhes "leader of four companies, tetrarch," from tetra- "four" (see tetra-) + arkhein "to rule" (see archon). Applied generally to subordinate rulers in the Roman Empire, especially in Syria.
strictly the ruler over the fourth part of a province; but the word denotes a ruler of a province generally (Matt. 14:1; Luke 3:1, 19; 9:7; Acts 13:1). Herod and Phasael, the sons of Antipater, were the first tetrarchs in Palestine. Herod the tetrarch had the title of king (Matt. 14:9).