The great hallmark of the New Covenant lies in the promise of God to forgive the sins of his people, a promise that simply did not pertain to the old covenant (Jeremiah 31:31-35); and, therefore, in Micah 7, we have a certain indication that the passage is Messianic.
The opening phrase, in that day, identifies what follows with the redemption of the remnant. This is the blessing of the redeemed; sin has been forgiven, and Jehovah is recognized and praised as the source of salvation.
This ten commandments covenant, the first and old covenant, is the one in view by the author of Hebrews is evident and becomes certain in the light of his mention of “the tables of the covenant” being placed within the ark of the covenant (Hebrews 9:4).
In Hebrews 8:6-7, this “new covenant” is contrasted with what is called “the first covenant,” or “the old covenant,” indicating that the new covenant would replace not merely those lesser covenants, but it would take the place of that covenant which was so great and comprehensive, overshadowing all others, that God called it the “first covenant.”