The namesake of his grandfather was briefly governor of the temple in Jerusalem after the death of his older brother, Agrippa I. Herod III was married first to his cousin, Mariamne [the daughter of Antipas' sister, Olympias & the son of Herod's brother Joseph], & then to his niece, Berenice [sister of Agrippa II]. The emperor Claudius gave him the Syrian kingdom of Chalcis at the foot of Mt. Hermon in the Lebanese mountains (ca. 42 CE). Though he never ruled Judea, he was granted authority over the temple with the hereditary right to appoint high priests. After his death, Claudius assigned his position & privileges to his nephew & brother-in-law, Agrippa II.

References: Josephus, Antiquities 18.133-137, 277-279, 288;
                                                        19.338-341, 353-354;
                                                        20.13-16, 103-104, 145.
                   _____, War 1.552; 2.217, 221-223.

Other resources on line: 

• Herod of Chalcis - entry in Wikipedia's web.

• Herod II - brief article in the 1906 Jewish Encyclopedia.