Rather than seeking human answers, let the Bible provide its own answer. Where is Jeremiah 31 quoted in the New Testament? Hebrews 8:8-12 quotes the prophecy in Jeremiah 31:31-34, showing its fulfillment and therefore its end.
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. [After quoting Jeremiah, it concludes,] In speaking of a new covenant, He makes the first one obsolete. And what is becoming obsolete and growing old is ready to vanish away. (Hebrews 8:6, 13)
What does “obsolete” mean? What comes to your mind? Outdated, archaic, no longer in use? Like papyrus scrolls went out of style when printing on paper took over. Does that mean the Old Testament or the Law of Moses is no longer useful? The Hebrew writer himself quotes them often to teach and encourage Christians. But, as a covenant, the Law no longer rules over God’s people. Its laws and conditions no longer apply, which explains why Christians do not follow Moses’ laws. As Jesus predicted, Jerusalem’s temple is no longer the worship center (John 4:21; Luke 21:5-6). Previously, God’s people were judged by those laws, but all that has changed.
[God canceled] the record of debt that stood against us with its legal demands. This He set aside, nailing it to the cross… Therefore let no one pass judgment on you in questions of food and drink, or with regard to a festival or a new moon or a Sabbath. These are a shadow of the things to come, but the substance belongs to Christ. (Colossians 2:14, 16-17)
The cross set aside the “legal” system that indebted and enslaved its people. Now, we enjoy a system of God’s grace. To impose old rules is to go backward, away from Christ (Colossians 2:19; Galatians 5:2-4).