When we read the beginning of the book of the Acts of the Apostles, we find Peter ready for the promised kingdom to Israel (Acts 1:8). The twelve are given a commission to go to the Jews first and are told to remain in Jerusalem until their message is received (Luke 24:47, Acts 1:8).
The final chapter of the book describes Paul in a far away Roman city sending salvation to the Gentiles while Israel had rejected Christ. He was the chief persecutor of Peter’s group until his conversion and did not have a ministry in Jerusalem.
Something happened by the end of the book that was not what Peter had in mind in Acts 1 or 2. While the ministry change is apparent, it seems that the nature of the change is often misunderstood.
It is often taught that the early church was mostly Jewish and after a time of incubation and growth it expanded out to Gentile countries. This is not what the scripture says as there was great persecution upon that church (Acts 8:1-3) and by Acts 28 the Jews had been cast away (Acts 28:28)!
It was only after the rejection of Peter’s message that Paul was given a special commission from Jesus in Acts 9. The specific ministry of grace to the Gentiles begins with Paul. (Peter’s singular ministry to a Gentile was in Acts 10 to Cornelius after Paul’s conversion, but it is with the gospel of the kingdom.)
After Acts 15 we do not hear about Peter anymore and Paul’s acts are the main subject. Paul was persecuted by his brethren because he taught Jesus Christ according to new information (Romans 16:25).
We can read what Paul taught in his ministry from reading his epistles. In them we find the doctrine of a new gospel that was “kept secret” and whereby Paul, a persecutor of the Jewish disciples of Christ, was saved by God’s longsuffering and not under a law system (Rom 3:22, 1 Tim 1:16).
Paul was the first to explain about a new dispensation from God (1 Cor 9:17, Eph 3:1). This major change in God’s administration makes for a surprise ending to the book of Acts. It also introduces the need for us to ‘rightly divide’ the scriptures when we read them. If we don’t, we will fall into salvation problems trying to reconcile Peter’s kingdom message with Paul’s message of grace is not a trivial matter.
This is why you may have heard right division referred to as mid-Acts or Pauline dispensational. A significant doctrinal and administrative change began with Paul in the middle of the book of Acts.