The new covenant is "new", as attested to by God (according to the writer of Hebrews).
In that He says, “A new covenant,” He has made the first obsolete. (Heb 8:13)
God used the word, "new" purpose when He told Jeremiah of the new covenant which was to come because He was indicating that the first covenant was going to be made obsolete. That's why one is called "old" and the other is called "new". The fact that the new covenant is better than the old covenant does not detract from the fact that it is new.
The old covenant made at Sinai
was not the commandments, but, on the part of the people, an
agreement to keep God's law (conditional), and on God's part a promise to give them certain blessings conditional upon obedience.
The law was that concerning which the covenant was made, but it was not the covenant itself. The weakness of this covenant was the fact that it was based on the principle, “Do and live,” whereas the people could not do, because they were carnal and trusted in the flesh, and therefore were unable to fulfill the covenant provisions. God knew that in their mere human strength they would be unable to keep it, and evidently the reason it was given was that it might serve as an everlasting lesson to man regarding his utter helplessness without God.
It has always been about do and live (reliance on the Lord) believing the Lord ... and still is. God does not change.
Hebrews 7:22
Because of this oath, Jesus has become the guarantee of a
better covenant.
Hebrews 8:6
Now, however, Jesus has received a much more excellent ministry, just as the covenant He mediates is better and is founded on
better promises.
Hebrews 8:8
But God found fault with the people and said: "Behold, the days are coming, declares the Lord, when I will make a new covenant with the house of Israel and with the house of Judah.
The salvation offered in the old covenant is the same offered in the new. (it would be fulfilled by Messiah - the better promise)
In the "new", however, a greater, more complete revelation of the God of the covenant and the love that He has for fallen humanity
has been revealed. It is better in that everything that had been taught through symbols and types in the Old Testament its fulfilment in Jesus, whose sinless life, His death, and high-priestly ministry were
symbolized by the earthly sanctuary service
(Hebrews 9:8-14).
The fact that the new covenant is better than the old covenant does not detract from the fact that it is new.
It does with some .... because some claim/teach the 10 commandments (moral laws) were done away with (became obsolete) and this is not so. There is nothing wrong with God's law that He should do away with it ... there was something faulty with the ceremonial sacrificial system as it had no redeeming qualities within it (ie blood of animals not sufficient) ... so the earthly sanctuary system was abolished.
The earthly sanctuary system became obsolete, (because the earthly sanctuary system never did have any redeeming qualities within itself) the law (10 commandments) did not become obsolete as some propose. The earthly sanctuary system was showing us how salvation would take place through the shed blood of Jesus.
We will all be judged ... to judge there must be law ... it is a lawful term. Those believing in redemption through Christ whether in ancient times (promise of Messiah to come - and He did) or now (promise of the Messiah to come again) will be saved .... it's the same promise as given in Genesis ... nothing new.
The lamb ... slain from the foundation of the world to take away sin is not new ... the salvation plan has always been in place (before creation) therefore not new. If it was in place before creation ... it's not new.
The law (the 10 moral law) was not abolished. The earthly sanctuary system was abolished.
Matthew 5:17-18 King James Version (KJV)Think not that I am come to destroy the law, or the prophets: I am not come to destroy, but to fulfil. For verily I say unto you, Till heaven and earth pass,
one jot or one tittle shall in no wise pass from the law, till all be fulfilled.
The law (the 10) are in place forever (the everlasting covenant) spans both Testaments ... not done away with.