Peter was only a simple fisherman but a devout Jew. He was very vocal. He was admonished by our Lord a few times. He was teachable and he readily and sincerely accepted and repented of all his mistakes.
After John the Baptist was imprisoned, he was sent out to continue to preach repentance to the Jews that the kingdom of heaven was coming soon.
At his confession of his faith that Jesus was the Messiah, he was given the keys to the kingdom of heaven.
Peter given Keys of the Kingdom
Mat 16:16-19 Simon Peter answered and said, "You are the Christ, the Son of the living God." Jesus answered and said to him, "Blessed are you, Simon Bar-Jonah, for flesh and blood has not revealed this to you, but My Father who is in heaven. And I also say to you that you are Peter, and on this rock I will build My church, and the gates of Hades shall not prevail against it. And I will give you the keys of the kingdom of heaven, and whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven."
The foundation of the church will be Jesus was the Christ (Messiah), the Son of God - so His finished work on the cross and His resurrection is the gospel of grace.
Peter was given the keys to the kingdom of heaven showing us that God had anointed him to sound doctrines for all believers.
After Peter had confessed that Jesus was the Messiah, our Lord taught them that the Messiah would not come as the King of kings to deliver Israel, but as a sacrificial Lamb of God. Just after His resurrection, our Lord commanded his disciples to preach the gospel of grace (message of the cross) to all men.
Luke 24:46-47 Then He (Jesus) said to them, "Thus it is written, and thus it was necessary for the Christ to suffer and to rise from the dead the third day, and that repentance and remission of sins should be preached in His name to all nations, beginning at Jerusalem."
Gospel of Grace to Jews
Acts 2:41 Then those who gladly received his word were baptized; and that day about three thousand souls were added to them.
Three thousand souls were baptised at Peter preaching the gospel of grace to the Jews.
Gospel of Grace to Gentiles
Act 10:46b-48a Then Peter answered, "Can anyone forbid water, that these should not be baptized who have received the Holy Spirit just as we have?" And he commanded them to be baptized in the name of the Lord...
Cornelius and family were baptized after hearing the gospel from Peter and God's gifts of tongue.
Gospel approved for Gentiles
Act 11:2-3 And when Peter came up to Jerusalem, those of the circumcision contended with him, saying, "You went in to uncircumcised men and ate with them!"
Jerusalem agreed that Gentiles were entitled to the same gospel of grace. Since then many Gentiles were saved.
Act 11:17-18 If therefore God gave them the same gift as He gave us when we believed on the Lord Jesus Christ, who was I that I could withstand God?" When they heard these things they became silent; and they glorified God, saying, "Then God has also granted to the Gentiles repentance to life."
No Law for Gentiles (Christians)
Act 15:24, 29 Since we have heard that some who went out from us have troubled you with words, unsettling your souls, saying, "You must be circumcised and keep the law" —to whom we gave no such commandment.
Apostle Peter preached to both Jews and Gentiles and the wisdom given to him helped the council in Jerusalem to make the law obsolete.
Christians are not allowed to keep any of the OT or Mosiac Law