The last verse of Galatians 3 tells us that the real children of Abraham were not the literal descendants of Abraham but rather the spiritual descendants. In other words the Israelites were a temporary unbelieving picture of the people of God. The real people of God are those for whom Jesus died and most of them are Gentiles.
If you belong to Christ, then you are Abraham’s seed, and heirs according to the promise. (Galatians 3:29 NIV)
Paul also mentions that the children of Abraham get the promise of the land of Canaan (Genesis 15:1-16, 17:1-8). The real believers get the true promise land that is heaven and the new heavens and earth, a land that will not end (Hebrews 4:1-11). It is with this in mind that Paul goes on to discuss in Galatians 4:1-7 the comparison of Israel under the Old Covenant with the real people of God under the New Covenant.
He begins by using a well-understood illustration in the Roman world of the relationship of the son in the household before and after he comes of age. Before he comes of age the son is subject to his guardian. Even though he is the heir he is treated like a slave until he comes of age. This refers to Israel under the Old Covenant and is described as referring to believers in their unbelieving state. As unbelievers we are in slavery to our sin.
What I am saying is that as long as the heir is a child, he is no different from a slave, although he owns the whole estate. He is subject to guardians and trustees until the time set by his father. So also, when we were children, we were in slavery under the basic principles of the world. (Galatians 4:1-3 NIV)
Paul goes on to describe the work of Jesus in his death on the cross to redeem those under law so that his people might receive the full rights of sons.
But when the time had fully come, God sent his Son, born of a woman, born under law, to redeem those under law, that we might receive the full rights of sons. (Galatians 4:4-5 NIV)
On the surface this might seem to be saying that Jesus died only for the Israelites under the Old Covenant. But this is exactly not what this passage is teaching. The argument of Paul’s letter to the Galatians is that when you add Mosaic Law keeping to the gospel message you end up with salvation by works (Galatians 1:6-9, 3:1-5, 3:10-14, 6:12-14). Paul is making the point that the Israelites were not real believers (except for a remnant) and it is only through the saving work of Jesus Christ on the cross is anyone saved and made part of the family of God. All true believers are made alive by the Holy Spirit and are children of God and heirs of eternal life
Because you are sons, God sent the Spirit of his Son into our hearts, the Spirit who calls out, “Abba, Father.” So you no longer are slave, but a son; and since you are a son, God has made you also an heir. (Galatians 4:6-7 NIV)
Paul is using an illustration of an heir before and after he comes of age to describe the difference between Israel produced by the Old Covenant and the real people of God produced by the New Covenant. He is making a comparison of unbelief with belief, slavery to sonship. This is Paul’s argument in Galatians. If you add the keeping of the Mosaic Law to belief in the cross of Jesus in order to be accepted by God or justified then you are putting yourself under the Old Covenant, a works covenant that cannot save you. The description of Jesus dying for those under the Old Covenant is made to drive home the point that the only way to be accepted by the Father is through the cross. This is especially true of the Israelites. Jesus died to redeem the elect of the Jews from the curse of the law. The Galatians misunderstood the role of the Mosaic Law and the Old Covenant in the plan of God. We, as true believers, have trusted in the saving work of Jesus Christ are not like the Israelites. We have the work of the Holy Spirit causing us to love our Lord and guaranteeing our perseverance (Romans 8:1-27). We are the true children of God and we are what Israel illustrated. The church has replaced Israel in the plan of God.