According to Luke in Acts 2
36 “Therefore let all the house of Israel know assuredly that God has made this Jesus, whom you crucified, both Lord and Christ.”
37 Now when they heard this, they were cut to the heart, and said to Peter and the rest of the apostles, “Men and brethren, what shall we do?”
38 Then Peter said to them, “Repent, and let every one of you be baptized in the name of Jesus Christ for the remission of sins; and you shall receive the gift of the Holy Spirit. 39 For the promise is to you and to your children, and to all who are afar off, as many as the Lord our God will call.”
19 Repent therefore and be converted, that your sins may be blotted out, so that times of refreshing may come from the presence of the Lord, 20 and that He may send Jesus Christ, who was preached to you before, 21 whom heaven must receive until the times of restoration of all things, which God has spoken by the mouth of all His holy prophets since the world began.
And Acts 3
17 “Yet now, brethren, I know that you did it in ignorance, as did also your rulers. 18 But those things which God foretold by the mouth of all His prophets, that the Christ would suffer, He has thus fulfilled. 19 Repent therefore and be converted, that your sins may be blotted out, so that times of refreshing may come from the presence of the Lord, 20 and that He may send Jesus Christ, who was preached to you before, 21 whom heaven must receive until the times of restoration of all things, which God has spoken by the mouth of all His holy prophets since the world began.
And Acts 15, still speaking of the future, well after the conversion of Paul. The times of refreshing is the restoration of Israel and the rebuilding of Jerusalem. And driving out the Romans while we are at. There is a catch in John 3, for later.
8 So God, who knows the heart, acknowledged them by giving them the Holy Spirit, just as He did to us, 9 and made no distinction between us and them, purifying their hearts by faith. 10 Now therefore, why do you test God by putting a yoke on the neck of the disciples which neither our fathers nor we were able to bear? 11 But we believe that through the grace of the Lord Jesus Christ we shall be saved in the same manner as they.”
Peter is looking forward to grace. As the covenant of circumcision is very hard burden to carry. And read the words of James very carefully. He speaks of the literal restoration and earthly kingdom of Israel. Peter and James belong to this church. They will sit in judgement over the tribes of Israel.
13 And after they had become silent, James answered, saying, “Men and brethren, listen to me: 14 Simon has declared how God at the first visited the Gentiles to take out of them a people for His name. 15 And with this the words of the prophets agree, just as it is written:
16 ‘After this I will return
And will rebuild the tabernacle of David, which has fallen down;
I will rebuild its ruins,
And I will set it up;
17 So that the rest of mankind may seek the Lord,
Even all the Gentiles who are called by My name,
Says the Lord who does all these things.’
It isn't just the gentiles, he will rebuild the tabernacle of David. As Daniel first told. As soon as you accept you are not part of Peter's church, the sooner you will understand. There are 2 New Testament churches. We have the same foundation, and nobody says otherwise. But we are appointed to heavenly places. The Jews are not. But, don't feel bad. They get a kingdom on the new earth. And it isn't like this hasn't been posted many times, but for the lurkers that only read, here it is again. From the prophet Daniel.
24 “Seventy weeks are determined
For your people and for your holy city,
To finish the transgression,To make an end of sins,
To make reconciliation for iniquity,
To bring in everlasting righteousness,
To seal up vision and prophecy,
And to anoint the Most Holy.
25 “Know therefore and understand,
That from the going forth of the command
To restore and build Jerusalem
The feasts have not been finished.