The apostle Paul talks about prayer more than anyone else in the entire New Testament.
The following are some of the passages of scripture where Paul prays or talks about prayer. In some of them, he requests prayer, in some he offers prayer. In others he reassures us of how Jesus is praying for us all the time. Please look up the following bible verses. As you look them up, understand that prayer is simply talking to God. It is communicating with God. This will help you realize that in some places, Paul just thanks God or shows an expression of it while in other places he talks in a more “formal” way.

Rom 1:8-10
Rom 10:1
Rom 12:12
Rom 15:5-6
Rom 15:13
Rom 15:30-33

1 Cor 1:4-9
1 Cor 16:23

2 Cor 1:3-7
2 Cor 2:14-16
2 Cor 9:12-15
2 Cor 12:7-9
2 Cor 13:7-9

Gal 6:18
Eph 1:3
Eph 1:15-23
Eph 3:14-21
Eph 6:19-20

Phil 1:3-6
Phil 1:9-11
Phil 4:6-7
Phil 4:23

Col 1:3-14
Col 4:2-4

1 Thess 1:2-3
1 Thess 2:13-16
1 Thess 3:9-13
1 Thess 5:23-24
1 Thess 5:28

2 Thess 1:3
2 Thess 1:11-12
2 Thess 2:16-17
2 Thess 3:2-5
2 Thess 3:16

1 Tim 1:12
1 Tim 2:1

2 Tim 1:3-7
2 Tim 1:16-18
2 Tim 4:22

Titus 3:15b

Philemon 1:4-7
Philemon 1:25