Definition:

The Law of Liberty = Belief and Trust, working through the love of God and love of man.

Galatians 5
Christ came for our freedom -
1It was for freedom that Christ set us free; therefore keep standing firm and do not be subject again to a yoke of slavery.
The law alone no longer saves us -

2Behold I, Paul, say to you that if you receive circumcision, Christ will be of no benefit to you. 3And I testify again to every man who receives circumcision, that he is under obligation to keep the whole Law.4You have been severed from Christ, you who are seeking to be justified by law; you have fallen from grace. 5For we through the Spirit, by faith, are waiting for the hope of righteousness. 6For in Christ Jesus neither circumcision nor uncircumcision means anything, but faith working through love.
- Here it is we find our definition of the Law of Liberty: Faith working through love.
Faith comes from the Greek, Pistis, meaning belief & trust.

The ten commandments, and thereby the whole Old Testament law, are given with two commandments of Love, love of God and love of man. Love is explained by the two great commandments in Matt 22:39:
37And He said to him, “ ‘YOU SHALL LOVE THE LORD YOUR GOD WITH ALL YOUR HEART, AND WITH ALL YOUR SOUL, AND WITH ALL YOUR MIND.’ 38“This is the great and foremost commandment. 39“The second is like it, ‘YOU SHALL LOVE YOUR NEIGHBOR AS YOURSELF.’ 40“On these two commandments depend the whole Law and the Prophets.”

Back to Galatians 5-

11But I, brethren, if I still preach circumcision, why am I still persecuted? Then the stumbling block of the cross has been abolished. 12I wish that those who are troubling you would even mutilate themselves.

13For you were called to freedom, brethren; only [do] not [turn] your freedom into an opportunity for the flesh, but through love serve one another. 14For the whole Law is fulfilled in one word, in the [statement], "YOU SHALL LOVE YOUR NEIGHBOR AS YOURSELF." 15 But if you bite and devour one another, take care that you are not consumed by one another.

16But I say, walk by the Spirit, and you will not carry out the desire of the flesh. 17For the flesh sets its desire against the Spirit, and the Spirit against the flesh; for these are in opposition to one another, so that you may not do the things that you please. 18 But if you are led by the Spirit, you are not under the Law. (.....) 22 But the fruit of the Spirit is love,joy, peace, patience, kindness, goodness, faithfulness, 23 gentleness, self-control; against such things there is no law. 24 Now those who belong to Christ Jesus have crucified the flesh with its passions and desires.

25If we live by the Spirit, let us also walk by the Spirit. 26Let us not become boastful, challenging one another, envying one another.

Full Scriptural Explanation of the Law of Liberty: Hebrews 8 - 10
(Read Context)

Putting the Law of Liberty into action. James 1
21Therefore, putting aside allfilthiness and [all] that remains of wickedness, in humility receive the word implanted, which is able to save your souls. 22But prove yourselves doers of the word, and not merely hearers who deludethemselves. 23For if anyone is a hearer of the word and not a doer, he is like a man who looks at his natural face in a mirror; 24for [once] he has looked at himself and gone away, he has immediatelyforgotten what kind of person he was. 25But one who looks intently at the perfect law, the [law] of liberty,and abides by it, not having become a forgetful hearer but an effectual doer, this man will be blessed in what he does.