A.T. Robertson 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)

After the reading of the law and the prophets (μετα την αναγνωσιν του νομου κα των προφητων). The law was first read in the synagogues till B.C. 163 when Antiochus Epiphones prohibited it. Then the reading of the prophets was substituted for it. The Maccabees restored both. There was a reading from the law and one from the prophets in Hebrew which was interpreted into the Aramaic or the Greek Koine for the people. The reading was followed by the sermon as when Jesus was invited to read and to preach in Nazareth (Luke 4:16f.). For the service in the synagogue see Schuerer, History of the Jewish People, Div. II, Vol. II, pp. 79ff. It was the duty of the rulers of the synagogue (αρχισυναγωγο) to select the readers and the speakers for the service (Mr 5:22,35-38; Luke 8:49; Luke 13:14; Acts 13:15; 18:8,17). Any rabbi or distinguished stranger could be called on to speak.

If ye have any word of exhortation for the people (ε τις εστιν εν υμιν λογος παρακλησεως προς τον λαον). Literally, if there is among you any word of exhortation for the people. It is a condition of the first class and assumed to be true, a polite invitation. On "exhortation" (παρακλησις) see 9:31. It may be a technical phrase used in the synagogue (Hebrews 13:22; 1 Timothy 4:13).