Yes, I believe this is a reference to the New Testament Law of Liberty referenced in James 2:12.
Look at the immediate context of Isaiah 51:4 (KJV).
1Hearken to me, ye that follow after righteousness, ye that seek the
Lord: look unto the rock whence ye are hewn, and to the hole of the
pit whence ye are digged. 2 Look unto Abraham your father, and unto
Sarah that bare you: for I called him alone, and blessed him, and
increased him. 3 For the Lord shall comfort Zion: he will comfort all
her waste places; and he will make her wilderness like Eden, and her
desert like the garden of the Lord; joy and gladness shall be found
therein, thanksgiving, and the voice of melody. 4 Hearken unto me, my
people; and give ear unto me, O my nation: for a law shall proceed
from me, and I will make my judgment to rest for a light of the
people. 5 My righteousness is near; my salvation is gone forth, and
mine arms shall judge the people; the isles shall wait upon me, and on
mine arm shall they trust.
The prophet’s instructions to those who follow after righteousness, is to go back to the starting place and that is the Promise to Abraham. God’s Promise to Abraham was an unconditional promise to love and bless Abraham and his seed just because God loves them. There was nothing required for Abraham but to believe God. Salvation/Righteousness starts with the Promise to Abraham.
In verse 4 Isaiah says that a law “shall” (future) proceed from me and (please note) “I will make my judgment to rest” (YLT: “…Peoples I do cause to rest”) to become a light of all the people. This is very important for this concept of rest connects with the Promise to Abraham as the New Testament tells us that God’s salvation is by grace/faith and not by the works of the Law. Here is a clear reference to the New Testament fulfillment of the Sabbath where Hebrews 4 tells us:
10 For he that is entered into his rest, he also hath ceased from his
own works, as God did from his.
The reference to a new law in Isaiah 51:4 connects to verse 7 of chapter 51:
7 Hearken unto me, ye that know righteousness, the people in whose
heart is my law; fear ye not the reproach of men, neither be ye afraid
of their revilings. 8 For the moth shall eat them up like a garment,
and the worm shall eat them like wool: but my righteousness shall be
for ever, and my salvation from generation to generation.
Isaiah references the law that is written upon the heart. In the Book of Romans chapter 2, Paul tells us that the law has been written on every human heart, whether Jew or Gentile.
11 For there is no respect of persons with God. 12 For as many as have
sinned without law shall also perish without law: and as many as have
sinned in the law shall be judged by the law; 13 (For not the hearers
of the law are just before God, but the doers of the law shall be
justified. 14 For when the Gentiles, which have not the law, do by
nature the things contained in the law, these, having not the law, are
a law unto themselves: 15 Which shew the work of the law written in
their hearts, their conscience also bearing witness, and their
thoughts the mean while accusing or else excusing one another;) 16 In
the day when God shall judge the secrets of men by Jesus Christ
according to my gospel.
In this passage, Paul states that both the Jew and the Gentile will be judged (guilty) by God’s law. The proof that the Gentiles (who did not receive the law) did in-fact have the law written on their hearts (just like the Jews) was the fact that the Gentiles demonstrated partiality, just like the Jews. Paul says the Gentiles either “accused” or “excused” one another. They “accused” someone if they acted/behaved just as they did and the “accused” someone if they acted differently then they did. In short, they demonstrated partiality. Because of their fallen nature, they judged the law written on their hearts with bias (respect of persons).
So, what is the answer? A circumcision of the heart! A circumcision of the heart will remove the physical law of Moses (bondage) and replace it with a spiritual law of liberty (freedom).
In Deuteronomy 30:6; God promises to unilaterally circumcise the heart of Israel.
6 And the Lord thy God will circumcise thine heart, and the heart of
thy seed, to love the Lord thy God with all thine heart, and with all
thy soul, that thou mayest live.
Here’s how Dr. Charles P. Bayliss (Dallas Theological Seminary) views this verse.
“The phrase ‘the LORD your God will circumcise your heart’ introduced
the New Covenant. The New Covenant was a change which God would enact
within man, as opposed to a change which man would accomplish on his
own.* Ezekiel 36 and Jeremiah 31 expanded Deuteronomy 30:6 further.
Thus Moses' final sermon to the nation prophesied a time when Israel
would return to covenant relationship, and God would change their
hearts. It was one of the earliest, most specific references to the
New Covenant. It is this return that is called ‘repentance.
*The Old Covenant was a test of man's ability to change his own heart. He was exhorted to "circumcise his heart" (Deut. 10:16; Jer. 4:4), but
he could not. The Old Testament records that failure. It is only in
the New Covenant that God changes man's old heart (cf. Col. 2:11; Rom.
Thus the new birth brought about a change in man where the law, written on the heart of man was removed. It was replaced by a new law, the law of liberty, the royal law.
8 If ye fulfil the royal law according to the scripture, Thou shalt
love thy neighbour as thyself, ye do well: 9 But if ye have respect to
persons, ye commit sin, and are convinced of the law as transgressors.
10 For whosoever shall keep the whole law, and yet offend in one
point, he is guilty of all. 11 For he that said, Do not commit
adultery, said also, Do not kill. Now if thou commit no adultery, yet
if thou kill, thou art become a transgressor of the law. 12 So speak
ye, and so do, as they that shall be judged by the law of liberty. 13
For he shall have judgment without mercy, that hath shewed no mercy;
and mercy rejoiceth against judgment.
So, the literal law requiring good works was replaced by a spiritual law of faith and love. For as James reminds us that all you have to do is transgress the law just one time and you will be guilty of all of it; a lifestyle that no one can live up to. So, James concludes, we should no longer live to or be judged by a law that brings death. However, we should live to and be judged by the Law that gives life/freedom, the law of liberty; for mercy rejoices against judgment (ie what you get when you transgress the Law of Moses).