From BiblePortal Wikipedia

Vine's Expository Dictionary of NT Words [1]

A — 1: Τετραρχής (Strong'S #5076 — Noun Masculine — tetraarches | tetrarches — tet-rar'-khace )

denotes "one of four rulers" (tetra, "four," arche, "rule"), properly, "the governor of the fourth part of a region;" hence, "a dependent princeling," or "any petty ruler" subordinate to kings or ethnarchs; in the NT, Herod Antipas,  Matthew 14:1;  Luke 3:19;  9:7;  Acts 13:1 .

B — 1: Τετραρχέω (Strong'S #5075 — Verb — tetraacheo | tetrarcheo — tet-rar-kheh'-o )

"to be a tetrarch," occurs in  Luke 3:1 (thrice), of Herod Antipas, his brother Philip and Lysanias. Antipas and Philip each inherited a fourth part of his father's dominions. Inscriptions bear witness to the accuracy of Luke's details.

Hastings' Dictionary of the Bible [2]

TETRARCH . The transliteration of a Gr. word ( tetrarchçs ) whose literal meaning is ‘the ruler of a fourth part.’ As a title it lost its strict etymological force, and was used of ‘a petty prince,’ or ‘the ruler of a district.’ In the NT ‘Herod the tetrarch’ is Herod Antipas, son of Herod the Great; he ruled over Galilee and Peræa (  Matthew 14:1 ,   Luke 3:1;   Luke 3:19;   Luke 9:7 ,   Acts 13:1 ), and is popularly styled ‘king’ (  Mark 6:14 ff.,   Matthew 14:9 ). Two other tetrarchs are mentioned in   Luke 3:1; viz., Herod Philip, the brother of Antipas, who ruled over the Ituræan and Trachonitic territory; and Lysanias, who was Tetrarch of Abilene ‘in the fifteenth year of Tiberius’ (see Schürer, HJP [Note: JP History of the Jewish People.] i. ii.,   Revelation 1 ).

J. G. Tasker.

American Tract Society Bible Dictionary [3]

Is strictly the ruler of the fourth part of a state or province; but in the New Testament it is a general title applied to those who governed any part of a kingdom or province, with an authority subject only to that of the Roman emperor. Thus Herod the Great and his brother were at one time, in early life, constituted tetrarchs of Judea by Antony. At the death of Herod the Great, he left half his kingdom to Archelaus, with the title of ethnarch; while the other half was divided between two of his other sons. Herod Antipas and Philip, with the title of tetrarchs. See Herod 1,2.

In the same manner Lysanias is also said to have been tetrarch of Abilene,  Luke 3:1 . It is Herod Antipsas who is called the tetrarch in  Matthew 14:1   Luke 3:19   9:7   Acts 13:1 . As the authority of the tetrarch was similar to that of the king, so the general term king is also applied to Herod,  Matthew 14:9   Mark 6:14 .

Smith's Bible Dictionary [4]

Tetrarch. Properly, The Sovereign or Governor Of The Fourth Part Of A Country.  Matthew 14:1;  Luke 3:1;  Luke 9:7;  Acts 13:1. The title was, however, often applied to Any One, Who Governed A Roman Province , of whatever size. The title of king was, sometimes, assigned to a tetrarch.  Matthew 14:9;  Mark 6:14;  Mark 6:22.

Fausset's Bible Dictionary [5]

Properly governor of the fourth part of a larger province and kingdom, i.e. a Tetrarchy . The title "king" is applied by courtesy, not right, to Herod "the tetrarch" ( Luke 3:1;  Mark 6:14). (See Herod .) As Archelaus was "ethnarch" over half of Herod the Great's whole kingdom, so Philip and Antipus had divided between them the remaining half, and were each "tetrarch" over the fourth; Herod over Galilee; Philip over Ituraea and Trachonitis; Lysanias over Abilene. Caligula annexed the three tetrarchies to the kingdom of Herod Agrippa I, whom he honoured with the title "king" (Acts 12).

Hastings' Dictionary of the New Testament [6]

This title originally signified the governor of the fourth part of a country. Thus Philip of Macedon divided Thessaly into four districts called ‘tetrarchies.’ Later, however, the title came to be used in a loose sense of any petty ruler, and in this sense it is applied in the NT to Herod Antipas, Philip, and Lysanias. Of these Herod is called ‘king’ in  Matthew 14:9; but the usual and correct designation of him is ‘tetrarch,’ and it is thus that he is mentioned in  Acts 13:1, the only passage in the apostolic writings where the title occurs.

G. Wauchope Stewart.

Morrish Bible Dictionary [7]

Literally the governor over a fourth part of a province, but also applied to the governor of any small province. It is employed in the N.T. in reference to Herod Antipas, tetrarch of Galilee and Peraea; Philip, tetrarch of Ituraea and Trachonitis; and Lysanias, tetrarch of Abilene.  Malachi 14:1;  Luke 3:1,19;  Luke 9:7;  Acts 13:1 .

Watson's Biblical & Theological Dictionary [8]

a sovereign prince that has the fourth part of a state, province, or kingdom under his dominion, without wearing the diadem, or bearing the title of king,  Matthew 14:1;  Luke 3:1;  Luke 3:19;  Luke 9:7;  Acts 13:1 .

People's Dictionary of the Bible [9]

Tetrarch. This title strictly denotes one who governs the fourth part of a province or kingdom.  Matthew 14:1. In Scripture, however, it is applied to any one who governed a province of the Roman empire, whatever portion of the territory might be within his jurisdiction.  Matthew 14:9.

Webster's Dictionary [10]

(1): ( a.) A Roman governor of the fourth part of a province; hence, any subordinate or dependent prince; also, a petty king or sovereign.

(2): ( a.) Four.

Easton's Bible Dictionary [11]

 Matthew 14:1 Luke 3:1,19 9:7 Acts 13:1 Matthew 14:9

King James Dictionary [12]

TE'TRARCH, n. Gr. four, and rule. A Roman governor of the fourth part of a province a subordinate prince. In time, this word came to denote any petty king or sovereign.

Holman Bible Dictionary [13]

 Luke 3:1Roman Law

Cyclopedia of Biblical, Theological and Ecclesiastical Literature [14]

( Τετράρχης , from Τέτταρα , Four, and Ἀρχή , Government), properly denotes the governor of a province or district which was regarded as the fourth part of a larger province or kingdom, while the district itself was called a tetrarchy ( Τετραρχία or Τετραδαρχία ). The earliest use of the word which seems to have been discovered is in connection with the division of Thessaly as originally constituted (Eurip. Alcest. 1154; Strabo, 9:5) and as reconstructed in the time of Philip of Macedon (Demosth. Phil. 3, 26), and of Galatia before its conquest by the Romans, B.C. 189. The first of these countries was then divided into four parts, each of which was named a tetrarchy, and its ruler a tetrarch, subordinate to the tagus (Thirlwall, Hist. of Greece, 6:13 sq.). The second was divided into three sections, each of which was again subdivided into four smaller ones, to which and to their governors the same terms were applied (Fischeri Prolusiones, p. 428, note); and these were ultimately fused into one Ἐπαρχία under Deiotarus, cir. B.C. 54 (Strabo, 566; Plutarch, De V. M. [ed. Wytt], vol. 2). In the later days of the Roman republic, and during the empire, the etymological meaning was almost entirely lost sight of, and it was applied, like "ethnarch" and "phlylarch," to the petty tributaries," the creatures of a proconsul's breath, and the puppets of his caprice" (Merivale, Hist. Of The Rom. 4: 167), whose importance did not warrant their receiving the title of "king" (see Sallust, Cath. 20:7; Cicero, Milo, 28:76; Vatin. 12:29; Horace, Sat. 1, 3, 12; Veil. Pat. 2, 51; Tacitus, Ann. 15:25). It is in this secondary sense that in all probability the word is used in the New Test. of the tetrarchs of Syria, the heirs and successors of Herod the Great. Niebuhr (Hist. of Rome, 2, 135) compares them to the zemindars of Bengal after their recognition by lord Cornwallis (179L-93) as proprietors of the soil, and enjoying some amount of sovereign rights within the limits of their zemiudary. The title of tetrarch was certainly given by Antony to Herod the Great in the early part of his career (B.C. 41) and his brother Phasael (Josephus, Ant. 14:13, 1), without reference to territorial divisions; and though it appears that the tetrarchs Antipas and Philip did actually receive a fourth part of their father's dominions, while Archelaus as "ethnarch" inherited half (ibid. 17:11, 4; War, 2, 6, 3), this correspondence of the name and the share may be considered accidental, or, at furthest, the exact use of the term in the New Test. must be confined to Antipas and Philip.

In the New Test. we meet with the designation, either actually or in the form of its derivative Τετραρχεῖν , applied to three persons:

1. Herod Antipas ( Matthew 14:1; Luke 3, 1, 19; Luke 9, 7;  Acts 13:1), who is commonly distinguished as "Herod the tetrarch," although the title of "king" is also assigned to him both by Matthew ( Matthew 14:9) and by Mark ( Mark 6:14;  Mark 6:22 sq.). Luke, as might be expected, invariably adheres to the formal title which would be recognized by Gentile readers. This Herod is described by the last-named evangelist (3, 1) as "tetrarch of Galilee;" but his dominions, which were bequeathed to him by his father, Herod the Great, embraced the district of Peraea beyond the Jordan (Josephus, Ant. 17:8, 1): this bequest was confirmed by Augustus ( War, 2, 6, 3). After the disgrace and banishment of Antipas, his tetrarchy was added by Caligula to the kingdom of Herod Agrippa I (Ant. 18:7, 2). (See Herod Antipas).

2. Herod Philip (the son of Herod the Great and Cleopatra, Not the husband of Herodias), who is said by Luke ( Luke 3:1) to have been "tetrarch of Itursea and of the region of Trachonitis." Josephus tells us that his father bequeathed to him Gaulonitis, Trachonitis, and Paneas (Ant. 17:8, 1), and that his father's bequest Nas confirmed by Augustus, who assigned to him Gaulonitis, Trachonitis, and Auranitis, with certain parts about Jamnia belonging to the "house of Zenodorus" (War, 1, 6, 3). Accordingly, the territories of Philip extended eastward from the Jordan to the wilderness, and from he borders of Persea northward to Lebanon and the neighborhood of Damascus. After the death of Philip his tetrarchy was added to the province of Syria by Tioerius (Ant. 18:4, 6), and subsequently conferred by Caligula on Herod Agrippa. I, with the title of king (ibid. 18:6, 10). (See Herod Agrippa I;) (See Herod Philip I.)

3. Lysanias, who is said ( Luke 3:1) to have been tetrarch of Abilene, a small district surrounding the town of Abila, in the fertile valley of the Barada or Chrysorrhoas, between Damascus and the mountain range of Antilibanus. (See Abilene). There is some difficulty in fixing the limits of this tetrarchy, and in identifying the person of the tetrarch. SEE LYSANIAS. We learn, however, from Josephus ( Ant. 18:6, 10; 19:5, 1) that a Lysanias had been tetrarch of Abila before the time of Caligula, who added this tetrarchy to the dominions of Hero Agrippa I an addition which was confirmed by the emperor Claudius.

Kitto's Popular Cyclopedia of Biblial Literature [15]

Tet´rarch, a prince or sovereign who holds or governs a fourth part of a kingdom, without wearing the diadem or bearing the title of king. Such was the original import of the word, but it was afterwards applied to any petty king or sovereign, and became synonymous with ethnarch.

In the reign of Tiberius Caesar Herod's kingdom of Judea was divided into three parts, which were called tetrarchies, and the sovereigns tetrarchs. His sons were made the heirs to his kingdom. Archelaus became tetrarch of Judea, Samaria, and Idumea; Philip of Trachonitis and Ituraea; and Herod Antipas of Galilee and Peræa . Herod Agrippa, the nephew of Herod Antipas, who afterwards obtained the title of king , was in the reign of Caligula invested with royalty, and appointed tetrarch of Abilene; to which was afterwards added Galilee and Peræa, Judea and Samaria; until at length his dominion extended over the whole land of Palestine [[[Herodian Family]]] The title of tetrarch was frequently conferred upon the descendants of Herod the Great by the Roman emperors.

International Standard Bible Encyclopedia [16]

tē´trark , tet´rark τετράρχης , tetrárchēs ): As the name indicates it signifies a prince, who governs one-fourth of a domain or kingdom. The Greeks first used the word. Thus Philip of Macedon divided Thessaly into four "tetrarchies." Later on the Romans adopted the term and applied it to any ruler of a small principality. It is not synonymous with "ethnarch" at least the Romans made a distinction between Herod "tetrarch" of Galilee, Philip "tetrarch" of Trachonitis, Lysanias "tetrarch" of Abilene, and Archelaius "ethnarch" of Judea ( Bj , II, vi, 3; Ant. , Xvii , xi, 4). The title was often conferred on Herodian princes by the Romans, and sometimes it was used courteously as a synonym for king ( Matthew 14:9;  Mark 6:14 ). In the same way a "tetrarchy" was sometimes called a kingdom.