From BiblePortal Wikipedia

Hastings' Dictionary of the New Testament [1]

This comparatively rare term is derived from ἔθνος, ‘a race,’ and ἄρχειν, ‘to rule’; perhaps the nearest English equivalent is ‘chief.’ The word is not known before the 2nd cent. b.c., and appears to indicate a ruler appointed by or over a people who were themselves part of a larger kingdom or empire, the appointment being made or recognized by its overlord or suzerain as valid. The purpose of such an appointment was perhaps primarily to safeguard the religion of a people. The earliest instance of an ethnarch known to us is that of Simon Maccabaeus. In  1 Maccabees 14:47 Simon accepts from the people the following offices-ἀρχιερατεῦσαι καὶ εἶναι στρατηγὸς καὶ ἐθνάρχης τῶν Ἰουδαίων καὶ ἰερέων καὶ τοῦ προστατῆσαι πάντων (‘to be high priest and to be general and ethnarch of the Jews and their priests and to rule over all’); and in  1 Maccabees 15:2 a letter of King Antiochus of Syria is addressed to him as ἱερεῖ μεγάλῳ καὶ ἐθνάρχῃ (‘great priest and ethnarch’). From  1 Maccabees 15:1-2 it is clear that the ἔθνος was the Jews themselves, and indeed almost everywhere where the term ‘ethnarch’ occurs, it refers to a ruler over Jews. Josephus ( Ant . xiv. vii. 2) shows us that the large Jewish community in the great city of Alexandria had an ‘ethnarch’ over it, and he defines his duties precisely thus: διοικεῖ τε τὸ ἔθνος καὶ διαιτᾷ κρίσεις καὶ συμβολαίων ἐπιμελεῖται καὶ προσταγμάτων, ὡς ἃν πολιτείας ἄρχων αὐτοτελοῦς (‘he governs the race and decides trials in court and has charge of contracts and ordinances as if he were an absolute monarch’).

An inscription (Le Bas-Waddington, Voyage archéologique en Grèce et en Asie Mineure , Paris, 1847-77, vol. iii. no. 2196 = W. Dittenberger, Orientis Grœci Inscriptiones Selectœ , Leipzig, 1905, vol. ii. no. 616) from a village, El-Mâlikîje in the Hauran, mentions by the names ‘ethnarch’ and ‘general ( or praetor) of nomads’ a chief of nomad Arabs of the time of Hadrian or Antoninus Pius who must have submitted to the Emperor.

These passages will help to illustrate the reference in  2 Corinthians 11:32. The man there mentioned was doubtless ruler of the Jews in Damascus and its territory, who were ‘permitted to exercise their own religious law very freely and fully’ (Ramsay, Pictures of the Apostolic Church , London, 1910, p. 90). He was under Aretas, who has the title βασιλεύς (‘king,’ i.e. of Arabia), and, indeed, as has been said, the ethnarch was always lower than a king. This fact is illustrated by interesting passages in Josephus ( Bellum Judaicum (Josephus) ii. vi. 3, Ant . XVII. xi. 4), where Caesar Augustus makes Archelaus not βασιλεύς, but ἐθνάρχης, of half of the territory that had belonged to Herod, promising him the higher title later, if certain conditions were fulfilled; and in Pseudo-Lucian (Macrob. § 17, ed. Jacobitz, Leipzig, 1896, vol. iii. p. 198), where a man is ‘proclaimed βασιλεύς instead of ἐθνάρχης of the Bosporus.’

A. Souter.

Hastings' Dictionary of the Bible [2]

Ethnarch is a Greek word translated by ‘governor’ in   2 Corinthians 11:32 . It is used also of Simon the high priest ( 1Ma 14:47; 1Ma 15:1-2 ). Its exact meaning is uncertain, but it appears to indicate the ruler of a nation or tribe which is itself living with separate laws, etc., amidst an alien race.

A. Souter.

Webster's Dictionary [3]

(n.) The governor of a province or people.

Cyclopedia of Biblical, Theological and Ecclesiastical Literature [4]

( Ἐθνάρχης ), properly Ruler Of A Nation; hence generally a praefect of a district or city (Lucian, Macrob. 17), e.g. Simon Maccabaeus, as head of the Jewish crommonwealth ( 1 Maccabees 14:47, "governor;" 15:1, 2, "prince;" Josephus, Ant. 13:6, 6); Archelaus, appointed lay his father's will and the emperor's ratification, his viceroy in Judaea (Josephus, War, 2:6, 3), of the national head (modern "Patriach") of time Jews in Egypt (Josephus, Ant. 14:7, 2; conp. Strabo, 16:798). Spoken of the "governor" or mayor of the city of Damascus ( 2 Corinthians 11:02), under the Arabian king Aretas (q.v.). (See Walch, Disert. in Acta Aposit. 2:85.)