The dates that are given to Paul’s conversion and the years following are as follows:
1. 33–36 are the years of his conversion on the way to Damascus and a short excursion to Arabia
2. At the end of the three years (approx. 36), he flees Damascus because of persecution; visits Jerusalem and meets with the apostles and brethren
3. For eight years, he preaches in Tarsus and the surrounding region (36–44)
4. In 44–46, he is invited by Barnabas to teach in Antioch
5. In 46, he visits Jerusalem with Barnabas to bring a famine relief offering
Paul persecuted the church (Gal 1:13–14; Acts 9:1–2; AD 34), was converted (Gal 1:15–16a; Acts 9:3–19a; AD 34), preached in Arabia and Damascus for three years (Gal 1:17; Acts 9:19–22, visited Peter and James in Jerusalem afterward (Gal 1:18–20; Acts 9:26–29), and preached in Judea for about ten years (Gal 1:21–24; Acts 9:30–31).
Fourteen years after his conversion (so it seems; cf. Gal 2:1 ), Paul took Barnabas and Titus to visit Jerusalem again for a private meeting with Peter, James, and John (Gal 2:1–10 ), which may or may not be recorded in Acts (if so, Acts 11:27–30; AD 47; this conclusion is debated and hinges on one’s interpretation of Galatians 2:1–10 and Acts 15:1–29).
Paul then went to the Jerusalem council in Acts 15:1–29 a year or so later (AD 49), an event probably not the same as what Paul records in Gal 2:1–10 (another debated issue). This conclusion is supported in that (1) Paul does not mention the Acts 15 conclusions in Galatians and (2) Luke describes the Acts 15 council as public (cf. Acts 15:6, 12, 22 ) while Paul describes Gal 2:10 as a private meeting (cf. Gal 2:2 ).
Paul then visited the Galatian churches two more times at the beginnings of his second (Acts 16:6; cf. cf. 15:40–18:22; AD 49) and third (Acts 18:23; cf. 18:23–21:17; AD 52) missionary journeys (AD 49–51 and 52–57, respectively).
So, if you are keeping track, (tentative) conclusions made were the following:
(1) Paul wrote the brethren in southern and not northern Galatia (i.e., the ones in Acts 13–14).
(2) Paul visited Jerusalem a second time fourteen years after his conversion and not fourteen years after his first visit to Jerusalem (Gal 2:1 ).
(3) Paul’s visit to Jerusalem in Gal 2:1–10 could be the one recorded by Luke in Acts 11:27–30.
(4) Pauls’ visit to Jerusalem in Gal 2:1–10 was probably not the one recorded by Luke in Acts 15:1–29.
(5) Peter visited Paul in Antioch (Gal 2:11–14 ) after Paul’s return to the city.
As one can see, it is sometimes very difficult to identify Paul’s locations and the times he was there with certainty and precision. While it is not imperative to figure out the timing of (5) (i.e., before or after Acts 13–14), it does seem that a combination of (1), (2), (3), (4), and (6) lean upon one another and, if one conclusion is made, so also are the others in this combination.
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.
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).