Where does the justification for The New Testament doers of the law in Romans 2:13 originate from?

If one puts new wine in old wineskins, the old wineskins will burst and all the wine is lost. To preserve new wine, one must employ new wineskins.
It is used to describe the new and old covenants. There is a temptation to some to try to keep part of the old covenant and adapt the new covenant to it. This invariably leads to error and confusion. Generally it centers around the law and the attending requirements of it.
This of course is what some are doing here. They cannot let go of the law. They would put us all back under the old covenant with some adaptations. Unfortunately, despite their objections, they are still trusting in their keeping of the law as a means to relate to God. Rather than accept the grace of God and the work of Christ on their behalf, they continue to work to gain acceptance with God. This is putting new wine in old wineskins. It bursts because this approach to peace with God will always fail.

Because we can and do grieve or quench the Spirit.

Christ said the law still exists.

Matt 5:18 For verily I say unto you, Till heaven and earth pass, one jot or one tittle shall in no wise pass from the law, till all be fulfilled.

The law still exits. Now with the New Covenant God has given us his Holy Spirit to guide us on how to follow the law.

The Bible says it is not hard to follow the Law. I believe when we listen to the Holy Spirit it will be even easier.

I have not seen anyone say it does not exist.

The law is impossible to follow if that is our motive(quenching the Spirit.) If our motive is to be filled with the Spirit and walk in the Spirit we follow the law perfectly.....but we can and do grieve or quench the Spirit. 1 John 1:9 is for us to get back in fellowship.

There are around 1000 commands/laws in the new testament. At any given moment, are you AWARE of every single command? Not likely.

But when we are filled with the Spirit and walking in the Spirit.....ALL of them are followed.

So with the Holy Spirit it is easier to find a priest to accept your sacrificial lamb? Um, no.

Christians are not under the Sinai covenant, aka “the Law”.

Period.

What is the result of following the Law?

Actually the Gentiles did have some specific Laws to abide by. Acts 15:
19 Wherefore I judge that we trouble not them that from among the Gentiles are turning to God,

20 but that we write to them to abstain from the pollutions of idols, and from sexual lewdness, and from what is strangled, and from blood.

This even exists today.

Us freely choosing to obey The New Testament Law shows our love for Almighty God.

We are under The New Testament Law.

There are no levite priests and no temple for sacrifices today. That does not mean they will not start again someday.

Eze 44:1 Then he brought me back the way of the gate of the outward sanctuary which looketh toward the east; and it was shut. 2 Then said the LORD unto me; This gate shall be shut, it shall not be opened, and no man shall enter in by it; because the LORD, the God of Israel, hath entered in by it, therefore it shall be shut. 3 It is for the prince; the prince, he shall sit in it to eat bread before the LORD; he shall enter by the way of the porch of that gate, and shall go out by the way of the same.

Eze 45;22 And upon that day shall the prince prepare for himself and for all the people of the land a bullock for a sin offering.

You mean the Law of the Spirit of Life, right? The one that sets us free from the law at Sinai?

"For in Christ Jesus the law of the Spirit of life set you free from the law of sin and death."

The law of the Spirit of life is the same law that was present before creation and it goes like this: God is our Father and we are His children. In us He put His Spirit. The Spirit testifies with our spirits that we are God's children and that we carry the nature of our Father inside of us.

This is like the natural agreement between a loving father and a newborn baby: nothing is written because it is the father's love for the child that secures his or her safety, joy, and fullness of life.

And what do we get for showing our love for God by obeying the law?

Depends, Are they following it by their own self-righteousness or is the Holy Spirit in them guiding them.

Give me both outcomes.

We get irritated because our wild little brother still gets a fatted calf celebration.

If you follow the law on your own no matter how much you feel you are following the law then you are not following the law. We need the Holy Spirit to show us the correct way to follow the law. The Pharisees thought they were following the law and Christ showed them that they were not.

Irrelevant. They don't exist. We couldn't follow the Law even if we were under it... which we are not.

John 8:36 plus Romans 8:2 If the Son sets you free, you will be free indeed. For in Christ Jesus the law of the Spirit of life set you free from the law of sin and death.