In Ac 13:7-8,12; 18:12, it denotes a proconsul; i.e., the governor of a Roman province holding his appointment from the senate. The Roman provinces were of two kinds, (1) senatorial and (2) imperial. The appointment of a governor to the former was in the hands of the senate, and he bore the title of proconsul (Gr. anthupatos). The appointment of a governor to the latter was in the hands of the emperor, and he bore the title of propraetor (Gr. antistrategos).
("proconsul" or "propraetor"); Greek anthupatos. The supreme governor of the provinces left by the emperors, still under the Roman senate (Ac 13:7; 19:38, plural for singular). The emperor gave the peaceable provinces to the senate. Over these the senate appointed those who had been praetors; governing only one year; having no power of life and death, not wearing sword or military costume (Dion. Cass., 53:13-14).
Achaia had been imperial, governed by a procurator, but was restored to the senate by Claudius (Tacitus, Annals 1:76; Suet., Claud., 25). So Gallio is rightly named "proconsul" or "deputy" (Ac 18:12). Cyprus after the battle of Actium was an imperial province (Dion. Cuss., 53:12), but five years later was given to the senate and had a deputy; so, Ac 13:7-8,12 is accurate. A coin of Ephesus, in the senate's province of Asia, illustrates the use of "deputies" in Ac 19:38.