Luke generally describes a meeting between Paul and the apostles in Acts 9:26–27. Paul gave more details as to this meeting in Gal 1:18–19. Paul mentions that he then left for Syria and Cilicia in Gal 1:21. Luke mentions this departure as Paul leaving for Tarsus in Acts 9:30 (Tarsus is a city in the region of Cilicia) and records his time in Antioch in Acts 11:25–26 (this was the Antioch in Syria; cf. Gal 1:21). Acts 22:17–21 records Paul’s recollection of a vision from Jesus during this time as well. What follows below is more detailed and chronological description of this time in Paul’s life. The passages above are cited, approximate dates are provided, and an explanation is given for why the accounts differ between Luke and Paul.
Three years after his conversion (AD 34), Paul came to Jerusalem for the first time as a believer (Gal 1:18; AD 37) and was rejected in his attempt to join the disciples―they were fearful that he was not truly one of them (Acts 9:26). But then Barnabas brought him to the apostles―Peter and James in particular―for a private, fifteen-day visit that, after an explanation by Barnabas of Paul’s ministry in Damascus, resulted in Paul’s fellowship with the brothers in Jerusalem (Acts 9:28a; Gal 1:18–19).
Having been granted this fellowship, Paul then preached boldly in Jerusalem and disputed against the Hellenists (Acts 9:28b–29a). As a result, these Hellenists sought to kill Paul (Acts 9:29b). At some point during this time, Paul was praying in the temple when Jesus appeared to him in a vision, warned him that the Hellenists would not accept his testimony, told him to leave Jerusalem quickly, and said that he would go far away to preach to the Gentiles (Acts 22:17–21).
Whether knowledgeable of Paul’s vision or not, the brothers in Jerusalem learned of the Hellenists’ plot to kill Paul, took him to Caesarea, and sent him to Tarsus in Cilicia (Acts 9:30), where Paul would begin to fulfill Jesus’ instructions. Paul was there for what may have been roughly eight of what many call his “silent years” (AD 37–45), ended by Barnabas retrieving him and bringing him to Syrian Antioch where he stayed for a whole year (Acts 11:25–26; cf. Gal 1:21; AD 45–46).
As to why Luke and Paul differ, Paul’s burden in Gal 1:11–2:14 was to explain that his gospel was from Christ and not Peter, the apostles, and Jerusalem. Paul explained the primary significance of his visits to Jerusalem along these lines but did not need to recount all of the details of his ministry during this time. As to Paul’s preaching in Jerusalem, Luke wanted to provide his readers with the reasons as to why Paul left for Tarsus (in Cilicia) and described how he eventually came to Antioch (in Syria).