How can christians say they live under the new covenant?

A covenant is an agreement. It speaks of a new covenant between God and Israel, in which he will bring them back to their own land, and they will all know Him as their God. I don't see anything in there that is relevant to the covenant of the New Testamant, after Jesus Christ's sacrifice. There can be many different covenants between God and different people. Think of it as the difference between *a* covenant and *the* covenant.