God chose Abraham out of all the human race and made of him the nation of Israel to be a kingdom of priests to eventually evangelize all of mankind when their Messiah sets up His kingdom. When their Messiah, Jesus Christ, came, He plainly told the twelve apostles that He was going to be killed and rise from the dead. But this was hidden from them by God, and they could not understand. The many Jews, who did not believe that Jesus Christ was the Messiah, crucified Him, and He was buried, and He rose from the dead and ascended into heaven. But the offer for Israel to receive their Messiah and kingdom remained open for a while longer if they would only believe that He was who He said He was. The twelve apostles led by Peter, preached the gospel of the kingdom to Israel, that Israel should believe that Jesus Christ was the Messiah, repent, and be baptized with water. If they all did this, then Jesus Christ would return and bring in the kingdom just as the Old Testament prophets had foretold. There was nothing in Peter’s message about departing from the law of Moses, to which the believing Jews adhered. Peter presented them the offer of the kingdom in the early chapters of Acts. But many in Israel still did not believe and rejected the ascended Lord Jesus Christ. But when Christ returns and purges the unbelieving two thirds (Zechariah 13:8-9), the remaining one third will all accept Him as their Messiah.
When they rejected the ascended Lord in the early chapters of Acts, God called Paul to be the apostle to the Gentiles. Up until that time, God had been dealing only with Israel, with just a few exceptions. Our ascended Lord Jesus Christ committed unto Paul the dispensation of the grace of God which had always been a secret hidden by God. This was a new program with new doctrine which God would show to Paul through many revelations. Paul was shown that the crucifixion of Jesus Christ had been the perfect sacrifice that paid for all of our sin, and that He had been raised from the dead for our justification. This is the gospel of grace, the gospel of our salvation today, which had before been a mystery, hidden by God. Under this present dispensation, we are saved by grace, through faith in the gospel alone, apart from the law of Moses or any other works. Even though Peter and Paul preached different gospels, there is no conflict between them because they dispensed their gospels to two separate audiences. So they were both correct. Peter preached kingdom doctrine to the Jews in the land of Israel, but Paul preached grace doctrine to the Gentiles in other countries and to the Jews scattered among them. When the destruction of the city Jerusalem and the temple came in 70 AD, the kingdom dispensation for Israel was put on hold, until it resumes in the future tribulation. But the grace doctrine for Jew and Gentile alike found in Paul’s letters of Romans-Philemon are directly applicable for the church today. source