Albert Barnes Commentary Acts 13:15

"And after the reading of the law and the prophets the rulers of the synagogue sent unto them, saying, Brethren, if ye have any word of exhortation for the people, say on." — Acts 13:15 (ASV)

And after the reading of the Law and the Prophets. See Barnes on Luke 4:16.

The rulers of the synagogue. These were persons who had the general charge of the synagogue and its service, to keep everything in order, and to direct the affairs of public worship. They designated the individuals who were to read the law; and called on those whom they pleased to address the people, and also had the power of inflicting punishment, and of excommunicating, etc. — (Schleusner). Mark 5:22, 35, 36, 38; Luke 8:49; Luke 13:14; Acts 18:8, 17.

Since Paul and Barnabas were Jews, though strangers, they sent to them, supposing it probable that they would wish to address their brethren.

Men and brethren. An affectionate manner of commencing a discourse, recognizing them as their own countrymen, and as originally of the same religion.

Say on. Greek, Speak.