Hebrews 8 transitions from Christ's superior priesthood (Chapter 7) to His superior ministry within a superior covenant. It functions as the central hinge of the book's argument, establishing the theological basis for why the New Covenant in Christ's blood renders the Old Covenant system obsolete. The author uses a lengthy quote from Jeremiah 31 as the definitive scriptural proof that God Himself had always planned to replace the first covenant with a new, better, and final one, marked by internal transformation and complete forgiveness.
Jesus guarantees a better covenant, a better relationship with God. And because he lives forever at God’s right hand, “he is able to save completely those who come to God through him” (7:25). The old covenant priests could not save anyone, but Jesus is fully effective at what they could only picture. Jesus does it not by adding himself to the old covenant, but by fulfilling the old so thoroughly that the old becomes unnecessary. He supersedes the old covenant, replacing it with a better covenant (7:22).