A Better Covenant With Better Promises
The general pattern of religion is a sort of contract with God – 'if you do 'x' for me then I will do 'y' for you. That was the style of the Old Covenant – the Law of Moses. Obeying God brought blessing (Deuteronomy 28:1-2), and disobedience resulted in being cursed (Deuteronomy 28:15). That Law certainly helped restrain evil behaviour but it could never change people's hearts. It also provided a limited forgiveness and another chance to do better. It prescribed that priests could only come from the tribe of Levi. But Jesus came from the tribe of Judah, so He could not be a Levitical priest or offer sacrifices under the old covenant.
The old covenant could never bring the righteousness which pleases God. That needed a new covenant. Romans 3:21-25 describes it: "But now apart from the law the righteousness of God has been made known, to which the Law and the Prophets testify. This righteousness is given through faith in Jesus Christ to all who believe. There is no difference between Jew and Gentile, for all have sinned and fall short of the glory of God, and all are justified freely by his grace through the redemption that came by Christ Jesus. God presented Christ as a sacrifice of atonement, through the shedding of his blood – to be received by faith. He did this to demonstrate his righteousness, because in his forbearance he had left the sins committed beforehand unpunished."
So the priesthood of Jesus was different from that of the Levites and ministered under a different covenant. The promise of eternal life for all who trust in Jesus is infinitely better than the Law of Moses (Hebrews 7:19). But the pattern of the old covenant does help us to see the seriousness of sin, the need for sacrifice and priestly mediation, and access to the Holy Place. It is just that Jesus does it all perfectly. It does not rely on human action but on Christ's action on our behalf. In every way, His ministry is superior – and it is completely effective in enabling sinful people to become righteous.
Yet we are often too religious, preferring to devise our own schemes for pleasing God rather than accepting His plan of salvation by faith in Christ. Yes, we may have started in grace but easily go back to thinking that it is what we do which pleases God, rather than who we are in Christ. We need to understand afresh that, "… if anyone is in Christ, he is a new creation; the old has gone, the new has come! All this is from God, who reconciled us to himself through Christ …" (2 Corinthians 5:17-18). Religion can only condemn: the grace of Christ is what we need. Consider: what is your confidence in God built on? Your efforts or His grace. Don't go back to the Law. Only the new covenant in Christ's blood will bring the life and peace you need.