Matthew Poole and continuators on Galatians 4:5

5 To redeem then that were under the law , that we might receive the adoption of sons .

This makes it appear, that Christ's being under the law must be understood as well of the Moral as of the Ceremonial Law, that is, subject to the precepts of it, as well as to the curse of it: For if the end of this being born under the Law, was to redeem those that were under it, that he had not reached by being merely under the Ceremonial Law, For the Gentiles were not under that Law, but only under the Moral Law;

and they also were to be redeemed, and to receive the great priviledge of Adoption, or rather, the rights of adopted children; which (some think) is to be understood here, rather than what is strictly to be understood by the term of Adoption, viz. a right to be called, and to be the Sons of God. Others by Adoption understand that full state of liberty which the Apostle had been before speaking, in opposition to that state of childhood and non-age in which believers were until the times of the Gospel; for chap. 5.1. we shall find that that was a liberty wherewith Christ made us free: And indeed this last sence seemeth best to agree with what the Apostle had before said, ver. 1, 2, 3. (though the other senses are not to be excluded.)

Marginal references: Joh. 1.12, chap. 3.26.