Paul travels to Rome, surviving a shipwreck at Malta on the way. He’s placed under house arrest in Rome for two years, a time he uses initially for explaining himself and the gospel to the local Jews: Acts 27–28
Perhaps in an attempt to head off trouble before it started, Paul invited the Roman Jewish leaders to hear his version of events. He didn’t mention the conspiracy to kill him, and the Jewish leaders had heard nothing specific, other than the trouble this new sect was stirring up.
So Paul was free to explain the gospel to them. Some believed, some didn’t, and Paul laid out his plans:
Acts 26:28-29 So I want you to know that this salvation from God has also been offered to the Gentiles, and they will accept it.
Whatever happened next, there was no further trouble with the Jewish leadership, even from those who chose not to believe because:
Acts 26:30-31 For the next two years, Paul lived in Rome at his own expense. He welcomed all who visited him, boldly proclaiming the Kingdom of God and teaching about the Lord Jesus Christ. And no one tried to stop him.
And that’s it. It’s the last we’re told about Paul in the book of Acts.
Church tradition, supported by a letter from Ignatius, suggests he was martyred somewhere, possibly Rome. Other writings, for example that of Clement in AD 95, suggest Paul was released from gaol and then continued his evangelism on a final missionary journey, possibly including a visit to Spain, before being rearrested and eventually martyred in Rome somewhere around AD64–68.