God comforts us by the oath He made to Christ, appointing Him our high priest forever after the order of Melchizedek.
Hebrews explains to us that a New covenant was necessary, because the old covenant was faulty. The fault, of course, lies in poor sinners, who cannot keep the old covenant, because of the fall, and their corrupt sin nature. The blessings of the old covenant therefore cannot be obtained.
Therefore, God discloses His New covenant, that brings His people salvation, not by our works or obedience, but by God's unilateral promise to us.
Hebrews goes to precise lengths to explain, that this New covenant is NOT LIKE the old covenant, which God made when Israel was redeemed out of Egypt, which covenant they promptly broke.
The New covenant is very different indeed! It is all of God's promise to us, and none of our promises to God. Salvation, and forgiveness, and sanctification, are not of our works, but of God's divine power working in us.
God promises new, changed hearts, intimate knowledge of Him and His law, and restoration of our mutual relationship unto God. Under this new covenant, God owns us, claims us, acknowledges us as His people, and we will do likewise toward our God.
The keystone, of course, is the promised forgiveness of our sins by God. He will be merciful to our unrighteousness! The curse of the broken law will be taken away.
This forgiveness and mercy to our unrighteousness was, of course, executed and empowered by the sacrifice our high priest, the Lord Jesus, made for us at Calvary. His is the blood of the New covenant, shed for His people for the remission of our sin.
Hebrews goes on to assert, that the old covenant is done away for us.