2 occurrences in 2 dictionaries

Reference: Asiarchs

Fausets

CHIEF OF ASIA (Ac 19:31). Officers, like the Roman aediles and Greek leitourgoi, yearly chosen by the cities in that part of Asia of which Ephesus was metropolis, to defray the cost and to undertake all the arrangements of the national games and theatrical sacred spectacles. Only wealthy persons could undertake the office. Each city chose one deputy, and out of the whole number ten were chosen, over whom one presided, selected by the Roman proconsul. The ten probably had the title, as well as the president, pre-eminently called "the Asiarchs." Ex-asiarchs also probably retained the title.

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Morish

A'siarchs

The word is ????????, 'chiefs of Asia.' They were officers chosen annually by the cities in the Roman province of Asia. They had charge of the public games and religious festivals. Ac 19:31. There were similar officers in other districts, as Syriarchs for Syria, etc. Some of the Asiarchs were friends of Paul and begged him not to endanger himself in the theatre: tumultuous mobs could not always be controlled.

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