After the reading of the law and the prophets, the officials of the synagogue sent them a message, saying, “Brothers, if you have any word of exhortation for the people, give it.” So Paul stood up and with gesture began to speak. Acts 13:15-16
Barnabas, Paul, and John have left Cyprus isle and traveled back to the mainland, to Perga in Pamphylia. After this, John Mark heads back to Jerusalem either for reason of being tired or wanting to avoid danger. Barnabas and Paul go North, about 50 miles, to Antioch in Pisidia. This is a different Antioch than was mentioned in verse 1.
They are in pagan (Gentile) territory where both physical dangers and hardships are now a reality. They are Spirit led. Synagogues are scattered throughout the Roman Empire and Paul chooses to accept the invitation to speak in synagogue, to give the Good News of Christ.
The whole Law is read once a year, and on the Sabbath a portion of the Law and a reading from the Prophets is read. After, these guests with a word from Jerusalem may speak openly. Paul is Spirit fed. Paul speaks the same that Stephen spoke before the Sanhedrin. He begins with Moses and the Exodus.
When you’re asked to speak a word, be led by the Spirit. Give it. Start with the heritage of the community and highlight common elements of faith then preach Christ– life of Christ, His Resurrection, and post-Resurrection appearances. Spoiler: in a weeks time the whole pagan city will come to hear Paul say it all again and hearts warmed by Christ will be Spirit wed.