Dam ha'brit, the blood of the covenant, is the exact phrase Moshe (Moses) spoke at Sinai when he took the blood of the offerings and threw it on the people: Behold the blood of the covenant, hineh dam ha'brit (Exodus 24:8). Watch what that blood does, because it is the opposite of what we usually assume blood is for. It does not cancel the covenant's terms or pay them off. It seals them. The blood thrown on the people binds the Torah they have just heard onto them; it ratifies the words, it does not retire them.

So when Yeshua lifted the cup and said this is My blood of the covenant, He was quoting Sinai whole. He was not announcing that the terms were now void. He was sealing them, the way the blood at Sinai bound. This is distinct from karat brit, to cut a covenant: the cutting establishes the covenant, and dam ha'brit is the blood that seals and binds its terms onto the people. And a thing that has just been sealed is precisely a thing that does not need sealing again.