The Law of the Gospel is the law of spiritual commandments. "Man shall live by every word that proceedeth out of the mouth of God". Not to long after Jesus had ascended into heaven the Holy Ghost was poured out upon the members of the Church. Everyone who was baptized into the Church was given the gift of the Holy Ghost by the laying on of hands. This gift is the gift to receive the word of God straight into ones own soul, as long as one lives worthy of this blessing.

The definition of living worthily is to earnestly strive to obey the law of carnal commandments (with the changes to it announced by Jesus and the Apostles), and the teachings of Jesus and the Apostles, and to live by the words of Jesus and the Apostles and the words of God as they are given to your own soul. Perfection is heard to attain, so when we fail to obey the will of the Lord, we must have our mind set to repentance, so that we won't be unclean any longer than we need to.

Many Christians would react to the idea of the law of carnal commandment being a part of Christian living. But it should not come as a surprice to anyone, since Jesus himself said:

17 Think not that I am come to destroy the law, or the prophets: I am not come to destroy, but to fulfill.

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.

19 Whosoever therefore shall break one of these least commandments, and shall teach men so, he shall be called the least in the kingdom of heaven: but whosoever shall do and teach them, the same shall be called great in the kingdom of heaven. (Matthew 5:17-19)

The way the Law and the prophets are fulfilled, to be overtaken by the law of the gospel, is on a commandment by commandment basis, and on a case by case condition. A Christian who doesn't live a chaste life must first go through the steps of contrite repentance, obedience and repentance being the very central themes of the law and the prophets. The Law of the gospel has added a vital element to repentance, namely a broken heart and a contrite spirit on behalf of the sinner. Before the law of the gospel the motivator of repentance was fear of God alone. Eventually, when the saving grace of Jesus has cleansed the sinner, when the fear of God is vanished, and the heart is no longer pained by guilt and sorrow, then the sinner is a sinner no more. As far as chastity goes s/he is now living the law of the gospel, being led by the Holy Ghost to stay clean, testifying about the blessings of chastity to others etc.

The person so repenting from a sin of the flesh is at the same time delivered from a host of other weaknesses by the grace of God. Thus we will find ourselves climb from level to level by the by repenting of the sins we commit.

The Law of the gospel is administered by the Higher Priesthood. The Law of Moses is administered by the Lesser Priesthood, or the Aaronic, or Levitical priesthood.  Since the law of Moses was given to a people with a lot of wickedness amongst them, the Levitical/Aaronic priests were not required to swear an oath of righteousness to God. God in his mercy knew that they would break such an oath and be cursed because of it. But the priest of  Melchisedec were spiritually mature, and in order to be blessed with this higher priesthood they were required to enter into a covenant with God to be obedient to his commandments;

11 If therefore perfection were by the Levitical priesthood, (for under it the people received the law,) what further need was there that another priest should rise after the order of Melchisedec, and not be called after the order of Aaron?

12 For the priesthood being changed, there is made of necessity a change also of the law.

13 For he of whom these things are spoken pertaineth to another tribe, of which no man gave attendance at the altar.

14 For [it is] evident that our Lord sprang out of Juda; of which tribe Moses spake nothing concerning priesthood.

15 And it is yet far more evident: for that after the similitude of Melchisedec there ariseth another priest,

16 Who is made, not after the law of a carnal commandment, but after the power of an endless life.

17 For he testifieth, Thou art a priest for ever after the order of Melchisedec.

18 For there is verily a disannulling of the commandment going before for the weakness and unprofitableness thereof.

19 For the law made nothing perfect, but the bringing in of a better hope did; by the which we draw nigh unto God.

20 And inasmuch as not without an oath he was made priest:

21 (For those priests were made without an oath; but this with an oath by him that said unto him, The Lord sware and will not repent, Thou art a priest for ever after the order of Melchisedec:) (Hebrews 7:11-21)

Salvation does not come by the Law of Moses. But in the ordinances of the Melchisedec Priesthood, which administers the Law of the Gospel, there is salvation to be found, in and through the atoning sacrifice of Jesus Christ.