The New Testament uses the Old Testament by quoting it and by alluding to it. Far more allusions than quotations are present. The biblical authors expect us to be knowledgeable of the Old Testament if we are going to notice the many allusions present in the New.
Some allusions stick out more than others. When Jesus is sitting with his disciples at the last supper and says, “This cup that is poured out for you is the new covenant in my blood” (Luke 22:20), the phrase “new covenant” should be like flashing lights for our eyes and mind. There is one place in the Old Testament where the phrase “new covenant” is found: Jeremiah 31.