By Acts chapter 9, Luke has already turned his attention to Paul, whom he’ll follow through most of the rest of the book. So why does Acts chapters 9-11 quickly turn back to Peter?
It is because this was a tremendous watershed moment in the life of the church. Up until now the church was comprised of only Jews or Gentiles who had already converted to Judaism and then to Christianity. No true Gentiles had believed yet. We find out in the first part of chapter 9 that Saul (or Paul as we know him) is going to be God’s witness to the Gentiles, but he apparently doesn’t share this with anyone for at least three years as he explains in Galatians 1.