Verse 6 would seem to take us straight to the heart of this chapter. Verses 1-5 describe how “the ministry Jesus has received is superior” to that of the priests that came before him, and verses 7-13 show how “the covenant of which he is the mediator is superior to the old one”
Jesus’ ministry is shown to be superior because of where he serves: not on earth in “a sanctuary that is a copy and shadow of what is in heaven”, but in “the true tabernacle” in heaven itself. That he serves there, representing us there as our high priest, means that we are accepted there, able to draw near there. Indeed he has “sat down at the right hand of the Majesty in heaven”. Imagine a priest entering the Holy of Holies on the Day of Atonement, sprinkling blood on the Atonement Cover, then sitting down on Ark of the Covenant and shouting out to everyone outside – “You can come in now!” Of course it could never happen, he had to leave and the curtain remained. But Jesus entered heaven itself and sat down, assuring us that we can now draw near to God through him.
As a priest is necessary for sinful people to have a relationship with God, so a covenant describes the terms of that relationship. Jesus, as the better priest, introduces a new kind of relationship, and therefore a better covenant. That God had spoken through Jeremiah of a new covenant was a sure sign that the old covenant was flawed.It was flawed because the people were flawed – “God found fault with the people” (v.8). The people could never keep the terms of the old covenant, so instead of knowing God’s blessing, they faced his judgment (v.9). The old covenant could never deliver perfection (7:11), because it required human obedience to make it work, and sinners are no good at obedience. This new covenant does deliver perfection – see v.11which describes the end for which we were made: relationship with God, knowledge of him that is personal , unmediated, and enjoyed equally by all God’s people.
This new covenant works because it is sin–proof, dealing with sin radically and completely. God’s character is implanted in our hearts (v.10), so that we love what He loves, and recoil from what He hates. The root of sin is our corrupt hearts, but under the new covenant we are given new hearts and are changed from the inside. Through the gift of the Spirit that has begun, a new nature has been implanted, and one day the transformation will be complete as all trace of the old nature is eradicated. Moreover, our sins are forgiven (v.12). How our sin has been dealt with will be explained in the chapters following: it is through the perfect sacrifice Christ offered.
John Chapman well sums up what is new about the new covenant under three headings –
(i) Religion is no longer a rule book [in the sense of an external code, for the law is written on our hearts], (ii) God is no longer a stranger, and (iii)Sin is no longer remembered [“remember” often has the sense in the Bible of to act on the basis of something in the past, as when God remembered his promised – it’s not that He had forgotten them, but that acts on the basis of them. Sin is no longer remembered because God will never treat us now as our sins deserve.]