Jesus was born into the Old Testament Church days when HE began HIS life as a man walking on this earth. HE began teaching what the NT church would be. The NT church came to be these doctrines of Jesus after the crucifixion and resurrection of Jesus.
Then from heaven, Jesus gave ministries to the NT church.
Ephesians 4
8 Wherefore HE saith, When HE ascended up on high, HE led captivity captive, and gave gifts unto men.
9 (Now that HE ascended, what is it but that HE also descended first into the lower parts of the earth?
10 HE that descended is the same also that ascended up far above all heavens, that HE might fill all things.)
11 And HE gave some, apostles; and some, prophets; and some, evangelists; and some, pastors and teachers;
12 For the perfecting of the saints, for the work of the ministry, for the edifying of the body of Christ: (through the New Testament Church)
13 Till we all come in the unity of the faith, and of the knowledge of the Son of God, unto a perfect man, unto the measure of the stature of the fulness of Christ:
14 That we henceforth be no more children, tossed to and fro, and carried about with every wind of doctrine, by the sleight of men, and cunning craftiness, whereby they lie in wait to deceive;
15 But speaking the truth in love, may grow up into HIM in all things, which is the head, even Christ:
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The New Testament Church comes after Jesus is taken back into heaven, after HIS death on this earth and the resurrection of Jesus where HE is taken back into heaven.
God speaks to Ezekiel of that New church that will come:
Ezekiel 36
23 And I will sanctify MY great name, which was profaned among the heathen, which ye have profaned in the midst of them; and the heathen shall know that I am the LORD, saith the Lord GOD, when I shall be sanctified in you before their eyes.
24 For I will take you from among the heathen, and gather you out of all countries, and will bring you into your own land.
25 Then will I sprinkle clean water upon you, and ye shall be clean: from all your filthiness, and from all your idols, will I cleanse you.
26 A new heart also will I give you, and a new spirit will I put within you: and I will take away the stony heart out of your flesh, and I will give you an heart of flesh.
27 And I will put MY spirit within you, and cause you to walk in MY statutes, and ye shall keep MY judgments, and do them.
Then circumcision avails nothing, for faith in Jesus replaces circumcision of the Old Testament. Now we are baptized into Christ ... dead to this world that we live by faith in Jesus, the Word.
Galatians 2
16 Knowing that a man is not justified by the works of the law, but by the faith of Jesus Christ, even we have believed in Jesus Christ, that we might be justified by the faith of Christ, and not by the works of the law: for by the works of the law shall no flesh be justified.
20 I am crucified with Christ: nevertheless I live; yet not I, but Christ liveth in me: and the life which I now live in the flesh I live by the faith of the Son of God, who loved me, and gave HIMSELF for me.
After Christ died for us, HE came to live in us.
Galatians 3
2 This only would I learn of you, Received ye the Spirit by the works of the law, or by the hearing of faith?
3 Are ye so foolish? having begun in the Spirit, are ye now made perfect by the flesh?
Galatians 5:2 Behold, I Paul say unto you, that if ye be circumcised, Christ shall profit you nothing.
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As Jesus walked on the earth, they saw in HIM a very different set of rules from the rules set forth for the Old Testament church.
Then after Jesus was crucified they came to God through faith in the shed blood of Jesus. And the Holy Spirit of Jesus lived in those who believed in HIM.
So Paul lived in the Old Testament and after Jesus spoke to Paul on the road to Damascus, Paul lived in the New Testament church through Jesus.
For more then 2000 + years, the New Testament church has taken the place of the Old Testament Church through the blood shed by Jesus, and Jesus rules the NT church from heaven and calls those chosen by HIM from heaven and sets us all things for the NT church through the foundation of the life and the words HE spoke while HE lived in front of them as an example.
The apostle Paul lived at the end of the Old Testament and at the beginning of the church of the New Testament.
Today we are at the end of the New Testament Church where all things pertaining to this current earth will be accomplished and God will take the elect to the new heaven and new earth to live in new spiritual bodies ... and God will destroy this current heaven and earth by fire. (2 Peter 3:10)
Watch for the destruction of Jerusalem, for the end begins with that.
Luke 21:20-22 And when ye shall see Jerusalem compassed with armies, then know that the desolation thereof is nigh. 21 Then let them which are in Judaea flee to the mountains; and let them which are in the midst of it depart out; and let not them that are in the countries enter thereinto. 22 For these be the days of vengeance, that all things which are written may be fulfilled.