The Abrahamic covenant comes in a series of stages from Genesis 12 through Genesis 17, and it clearly points forward to Christ. In Genesis 12, God says to Abraham that in him, in his seed, the nations are going to be blessed. And when Paul picks that up, he sees that fulfilled in Jesus Christ. So, is the Abrahamic covenant still in operation?
It is still in operation in the sense that it has been fulfilled. The promise has been realized, and God has kept the promise that He gave to Abraham. And this is why, for example, Paul says in Galatians 3:13–14 that Christ became a curse for us in order that the blessings of the covenant that were promised to Abraham might now come to the Gentiles. I think the thing for us to understand is that the Abrahamic covenant is fulfilled in Jesus Christ.
Paul makes the point in Galatians that no matter our nationality—whether we are Jews or Gentiles—the covenant fulfillment to which we look is Jesus Christ Himself. The New Testament does not teach that there is one covenant for the physical seed of Abraham and another covenant for those who are not the physical seed of Abraham, as though there were two tracks of salvation being provided in the Bible. This is the importance of Paul emphasizing the way in which Christ fulfills the covenant by becoming a curse so that all may experience the blessings of the Abrahamic promise.
Ligonier Ministries