What does "having received authority from the chief priests" mean in Acts 26:10?
It means Paul had been given official authority from the chief priests, placing him in a position to carry out his persecution. The Greek word behind the phrase denotes authority, not mere strength. So his imprisoning of the saints in Jerusalem was done under delegated authorization from the chief priests.
Les explains that the same Greek word translated “power” elsewhere is the word for authority. In Acts 26:9–10, Paul describes his pre-salvation persecution: he thought he ought to do many things contrary to Jesus of Nazareth, and he shut up many saints in prison. “Having received authority from the chief priests” means he was put in a position where he could do what he was doing—he had authority. So it was delegated authority from the chief priests that enabled his actions against believers.
Which thing I also did in Jerusalem: and many of the saints did I shut up in prison, having received authority from the chief priests; and when they were put to death, I gave my voice against them.