The book of Acts ends with Paul’s first Roman imprisonment, from which he was eventually released and which was a comparative walk in the park.
Acts is the final historical book of the New Testament, so we must infer anything further about Paul’s life and ministry from his later letters. Without an independent witness to Paul’s travels, trials and tribulations, we only know what went on by reading between the lines of the apostle’s subsequent correspondence with local churches, friends and associates.
Everything we know about the circumstances of his second imprisonment comes from 2 Timothy.