One was, that it might serve as a schoolmaster to lead Israel to Christ (Galatians 3:24); and the other, to foreshadow a better or new law covenant arrangement which God would make through his beloved Son Christ Jesus.

(Hebrews 10:1; 8:5) Christ is the great high priest; and by his fulfilling the divine purposes, he is now the mediator of a better covenant, the new covenant, which God purposes to make for man's benefit.

(Hebrews 8:6; 9:15) When the church is glorified and the kingdom set up, then the blood (merit) of Christ will be applied for the sealing of the new covenant, through which covenant promised blessings are to be extended to the human race.
[554]After these days, then--after the gathering out of the Christ class or new creation--this covenant is to be made, as St.Paul states: "Behold, the days come, saith the Lord, when I will make a new covenant with the house of Israel and with the house of Judah; not according to the covenant that I made with their fathers in the day when I took them by the hand to lead them out of the land of Egypt; because they continued not in my covenant, and I regarded them not, saith the Lord.
For this is the covenant that I will make with the house of Israel _after those days_, saith the Lord; I will put my laws into their mind, and write them in their hearts; and I will be to them a God, and they shall be my people; and they shall not teach every man his neighbor, and every man his brother, saying, Know the Lord: for all shall know me, from the least to the greatest.

For I will be merciful to their unrighteousness, and their sins and their iniquities will I remember no more."-- Hebrews 8:8-12.
[555]Under this new covenant the whole human race shall have the opportunity to come back to God through Christ the mediator.

Mark that it is plainly stated that during the time of restoration 'God will put his laws into their minds, and write them in their hearts, and will be to them a God and they shall be to him a people; for he will be merciful to them, and their sins and iniquities he will remember no more'.