Acts 26:1. Then Paul stretched forth the hand, and answered for himself.
This was a customary form of dignified oratory, designed to show the earnestness of the speaker. The orator stretched forth the right hand, having the two lowest fingers shut in on the palm of the hand, while the other fingers were extended. It is said that Demosthenes often used this gesture.
This is not to be confounded with the “beckoning” mentioned in Acts 13:16. That was simply a motion of the hand for the purpose of gaining attention. See also Acts 12:17.