For he finds fault with them when he says:
“Behold, the days are coming, declares the Lord, when I will establish a new covenant with the house of Israel and with the house of Judah, not like the covenant that I made with their fathers on the day when I took them by the hand to bring them out of the land of Egypt. For they did not continue in my covenant, and so I showed no concern for them, declares the Lord. For this is the covenant that I will make with the house of Israel after those days, declares the Lord: I will put my laws into their minds, and write them on their hearts, and I will be their God, and they shall be my people. And they shall not teach, each one his neighbor and each one his brother, saying, ‘Know the Lord,’ for they shall all know me, from the least of them to the greatest. For I will be merciful toward their iniquities, and I will remember their sins no more.”
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 8:8-13, ESV)
The Law of Moses is an old covenant in doddering senility. Just as Aaron’s priesthood was never meant to be the final priesthood (Jesus is a priest forever after the order of Melchizedek), so the covenant that give’s Aaron’s priesthood life was never meant to be the final form of the covenant. From the very beginning God was committed to bringing a new phase to His covenant that is implied in Genesis 15, mentioned in Deuteronomy 30 and Ezekiel 37, and most clearly delineated in Jeremiah 31. And that is where our author goes to make his next point, that the old covenant is obsolete.
He merely quotes Jeremiah 31:31-34. Yahweh declares that He will establish a new covenant with Israel and Judah that is different from the old one in that it does not depend on the sinful hearts of people to keep it but instead puts His laws in their minds and hearts to enable them to keep them. And, He promises forgiveness of sins forever. These are the two provisions of the New Covenant, a new heart and total forgiveness.
If God only forgave us but did not give us the ability to keep His commands, we would continue in sin. If He only gave us new hearts but not forgiveness, we would continue in guilt. Just giving us a law does not enable us to keep it. In fact, Paul found the law to be death to him because of his inability to keep it (Romans 7).
When the temple was destroyed in A.D. 70 the old covenant in essence vanished away. Though Jews still celebrate the festivals there is no provision for the sacrifices required because there is no place they are allowed to offer them. Messianic Jews, on the other hand, who still celebrate the festivals, know that Jesus has provided the sacrifice. One day all Israel will recognize what Christ has offered and repent and be saved (Romans 11). The New Covenant’s other provisions, a land for Israel in which God dwells and Israel leads the nations, will also be fulfilled.
Our author is demonstrating that in Christ we have become partakers of the New Covenant. There is no benefit in returning to life under the old covenant. It is obsolete. For Gentile believers who are in Christ, we, by virtue of our relationship to Jesus, have been brought under the New Covenant as well. We have been given new hearts and forgiveness. Our covenant relationship with God can never be broken because He has made it unbreakable. True believers will persevere in faith because of God’s Spirit within us.