The Law does not annul or add to the Abrahamic Covenant, which is described by Paul as a Covenant of Promise. (Gal 3:15-18)
The Covenant made to Abraham was a promise to bless him and his offspring. This blessing consisted of two parts,
1) God would be their God, and
2) God would give them the land of Canaan for an everlasting possession.
Now again, these promises were made to Abraham and his seed, that is Christ. (Gal 3:16)
So entrance into this covenant of promise must be brought about by being in Christ. The Jews misunderstood this and thought that just because they were the physical descendants of Abraham that they would inherit the promises. And they did receive temporal blessings, which they to this day enjoy, because of this covenant. But we are to see that God made the promise of blessing to Abraham and Christ, as we look back from the New Covenant perspective that has been given to us by Christ and His Apostles. The Covenant of Law, which was given 430 years after Abraham received the Covenant of Promise, does not expand upon that Covenant. Neither does it take away from it. The question that Paul must answer in light of this is, “Why then the Law?” (Gal 3:19) Rather than say anything more on the twofold purpose of the Law, see here and here.
Now according to that first use of the Law, which is Paul’s main point in Galatians, the purpose of the Law was to conclude all under sin. In effect, the Law was a ‘uniter’ of all humanity under the guilt of Adam. So although we did not sin in the same way that Adam sinned, we are united under the same standard of guilt. (Rom 5:14)
So when it is said that Christ was born under the Law (Gal 4:4-5), there is an implication of Christ’s unity with mankind by virtue of being under the same standard. And like, Adam, who acted as the representative of all humanity in his rebellion, Christ acts as the federal head of those who will believe by His obedience to the Law which had previously condemned all.
The great purpose of the Law, then, is to unite us all under sin, so that the promise which was made to Abraham and to his Seed (Christ), may be granted to those who believe by virtue of their new union under the headship of Christ. (Gal 3:22-29, 4:4-6, Rom 5:12-21, Eph 1:3-14)