The sign of the old covenant was circumcision. There were other signs and symbols given by God to Israel to designate them as His own, but circumcision was the specific covenant mark. The sign of the new covenant is not baptism, at least it isn’t ever connected as such in the New Testament. While there are some similarities between the two initiating rites, especially that both happen at the beginning and ideally only once, nowhere do we read in the Bible about Christian baptism and a covenant.
We do, however, hear Jesus teaching about the connection between a meal and a covenant. “On the night when he was betrayed” He gave thanks to His Father and gave bread to His men. Then, giving thanks to His Father again, “he took the cup, after supper, saying, ‘This cup is the new covenant in my blood. Do this, as often as you drink it, in remembrance of me.’”
The old covenant was not as good. The author of Hebrews says “Christ has obtained a ministry that is as much more excellent than the old as the covenant he mediates is better, since it is enacted on better promises” (Hebrews 8:6). Then Hebrews quotes Jeremiah 31, leaving in all the parts about “the house of Israel and the house of Judah.”
The blood of Jesus acquired and sealed the new covenant promise. That does not, though, mean that Jesus’ blood finished the covenant. Obviously it didn’t. His word guaranteed it, His blood obtained it, and His Spirit will complete it.
So there is both an already and a not yet as well as an in addition. Those of the household of Israel who believed in the first century and centuries since are evidence of the beginning of what still will be finished, atonement and restoration. Gentiles also who believed in Paul’s day and in ours are evidence of God’s grace to extend salvation to the nations. This meal is a long session in the same direction.