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.