For Christ is the end of the law so that there may be righteousness for everyone who believes.
When Jesus cried out on the cross, “It is finished,” (John 19:30), not only did that mean his time and travail on the cross, but surely as well, and perhaps primarily, the work he had come to do, which would be vindicated by his resurrection from the dead.
What specifically was accomplished at that point was the end of the old covenant, and the beginning of the new covenant. This change is in terms of fulfillment and completion of the old, and out of that, the metamorphosis into the new.
Jesus by his death brought in a new order in which the requirement of the Law might be fully met in those who have faith and live according to the Spirit rather than the flesh (Romans 8). And so also is fulfilled the greater, deeper righteousness Jesus was talking about in the Sermon on the Mount. Far from relegating that sermon to a different time and people, the heart of it is fulfilled both in terms of the true meaning of the Law, and how it’s supposed to be lived out now. Of course we have to read that sermon in context, so that not every line in it lines up with today (e.g., the altar in it). But the essence of it is surely apt, fulfilled in the new covenant: an internal righteousness that goes right to the heart to change the life.
So there is both continuity and discontinuity. Surely a radical newness along with a fulfillment of the old covenant, which itself is actually called imperfect (Hebrews) and even flawed, seemingly because of its dependence on sinful humans for its fulfillment (Jeremiah). Jesus’s coming and specifically his death sealed in the new covenant, which is dependent on God and God’s promises fulfilled in Jesus and from that by the work of the Spirit mark the start of a new resurrection life, the new creation. If we doubt such a claim, thinking it too radical, and perhaps think that this awaits the after life, then we need to read again the entire New Testament and compare it with the Old Testament. All of this in and through Jesus.