Does a legal compilation of all laws included in the New Testament exist?

Yes. In the upper half verses of James Chapter 2, James covers the OT law of "respect of persons" (which is to show favoritism of one man over another and originates from OT Leviticus 19:15 and Deuteronomy 1:17). This is NOT one of the 10 commandments, but James goes on to quote two of the 10 commandments. He states that if you violated this first command of "having respect of persons" you violated the "whole law" which includes the 10 commandments and become guilty of all of them.

Though being guilty isn't the same as suffering judgement from that guilt. That's why Jesus was sent from God! 1 John 2:1-2

And if any man sin, we have an advocate with the Father, Jesus Christ the righteous: 2 And he is the propitiation for our sins: and not for ours only, but also for the sins of the whole world.

There is no consolidated list of "commandments" in the NT; however, all of the 10 commandments in the OT are repeated (some several times) in the NT. Leaving these aside, here is a very incomplete list of moral requirements set out in the NT.

• 1 Peter 1, 2 - holiness (1 Peter 1:15), Purity (v22), Obey the truth (v22), love (v22), “rid yourselves of all malice and all deceit, hypocrisy, envy, and slander of every kind” (1 Peter 2:1), abstain from sinful desires (1 Peter 2:11), submit to civil authorities (v13-17), see also Rom 13:1-7, etc.
• Regular and frequent prayer, 1 Thess 5:17, 1 John 5:16, 1 Chron 16:11, 2 Chron 7:14, Psalm 5:3, Mark 1:35, Eph 6:18, James 5:13, Matt 5:44, 26:41, Prov 15:8, Ps 17:6, 102:17, Rom 12:12, 8:26, Luke 18:1, Phil 4:6, Col 4:2, 1 Tim 2:1, 2, 8, 4:5, 1 Peter 4:7, etc, etc.
• Discipling of new people, Mat 28:19, Acts 1:7, 8. See “Discipling”.
• Celebration of the New Covenant via the Lord’s Supper/communion, etc. 1 Cor 11:23-29, Matt 26:26-30, Mark 14:22-26, Luke 22:15-23, John 13:2-17.
• Baptism following conversion: Matt 3:6, 13-17, Mark 1:9-11, Luke 3:21, 22; Acts 8:36-38, John 3:22, 23, 4:1, Acts 8:36, 38, 1 Cor 1:14, 16.
• Being generous to the poor, Ex 23:11, Prov 3:27, 28, 11:24, 25, 14:31, 17:5, 19:17, 21:13, 22:2, 9, 16, 22, 23, 28:3, 8, 27, 29:7, 13, 31:9, 20, Isa 10:1, 2, 58:1-21, Jer 7:3-6, Amos 4:10, Micah 6:8, Matt 23:23, Acts 4:32-35, Gal 2:10, James 1:27. More specifically, feed the hungry and thirsty, be hospitable to strangers, clothe the naked, care for the sick, visit prisoners, Matt 25:31-46.
• Hospitality, 1 Tim 3:2, Titus 1:8, Heb 13:2, 1 Peter 4:9.
• Providing the means, voluntarily, for the support of church ministry and outreach, Matt 10:10, Luke 10:7, 8, 1 Cor 16:2, 2 Cor 9:3-14 (including a believing wife, v5)
• Being just and fair, 2 Chron 19:6-10, Micah 6:8, Matt 23:23.
• Doing good to others, especially believers, Prov 3:27, 28, Prov 11:25, Luke 3:10, 11, 6:27-45, Gal 6:2, 9, 10, Col 3:23, Heb 13:16, 1 Peter 4:10, 11.
• Obey civil legal laws, including paying government taxes, Matt 22:21, Rom 13:1-7, 1 Peter 2:13-17.
• Keeping in good physical health, Rom 12:1, 1 Cor 6:19, 20, 3 John 2.
• Prohibition against eating blood, Acts 15:29 (See Noahide laws Gen 9:4-6, 17).
• Regular Christian gatherings of believers, Heb 10:24, 25.
• Being kind to, and providing for the needs of animals. Luke 14:5. (See also Prov 12:10, 27:23, Deut 25:4, etc)
• Caring and protecting the environment. Luke 12:22-48, Matt 24:45-51, 25:14-30, Luke 19:12-28, Rev 11:18.

There are many more but this illustrates how broad-ranging and encompassing is the Christian life who imitates Jesus.

When a Pharisee asked Jesus which is the greatest commandment in the Law, Jesus said this:

Hear, O Israel, the Lord our God, the Lord is one. Love the Lord your God with all your heart and with all your soul and with all your mind and with all your strength. The second is this: Love your neighbour as yourself. There is no commandment greater than these (Mark 12:29-31).

The first quotation is known as the Shema, named after the first word of Deuteronomy 6:4. To the Shema Jesus joined the commandment from Leviticus 19:18 to show that love for neighbour is a natural and logical development of love for God.

As recorded in Matthew 22:40, all the Law and the Prophets hang on these two commandments.

Jesus went a bit further with regard to the law to love your neighbour as yourself. He said:

But I tell you who hear me: Love your enemies, do good to those who hate you, bless those who curse you, pray for those who ill-treat you... Do to others as you would have them do to you... Be merciful, just as your Father is merciful (Luke 7:27-36).

The Ten Commandments were essentially a summary of the entire Old Testament law. Nine of the Ten Commandments are clearly repeated in the New Testament (all except the command to observe the Sabbath day). Obviously, if we love God, we will not be worshiping false gods or bowing down before idols. If we love our neighbours, we will not be murdering them, lying to them, committing adultery against them, or coveting what belongs to them. The Old Testament law was never intended by God to be the universal law for all people for all of time. We are to love God and love our neighbours. If we obey those two commands faithfully, we will be upholding all that God requires of us.

The answer to your question is that there is no list of New Testament laws.

Note: This view is from a Protestant Christian.