When discussing the biblical covenants there are those that point to Jeremiah 31 in Hebrews 8 to prove their point that the law in its entirety has been abrogated. They stop at verse 13 in chapter 8 and say see it has vanished away!
In that he saith, A new covenant, he hath made the first old. Now that which decayeth and waxeth old is ready to vanish away. Hebrews 8:13 (KJV)
But the question is: what is ready to vanish away? Hebrews 9 explains that it is the ceremonial aspects of the Old Covenant administration of Grace, that pointed to the remission of sins in the coming Messiah, that would vanish away. This ceremonial system was in place as a schoolmaster or tutor for the children of Israel until Messiah comes (see Galatians 3 and 4).
Which was a figure for the time then present, in which were offered both gifts and sacrifices, that could not make him that did the service perfect, as pertaining to the conscience; Which stood only in meats and drinks, and divers washings, and carnal ordinances, imposed on them until the time of reformation. Hebrews 9:9,10 (KJV)
Why? Because Christ would be the High Priest AND final sacrifice as the perfect Lamb of God that shed His blood once and for all His elect. No longer slaves to the ceremonial law, but now free as joint-heirs with Christ.
But Christ being come an high priest of good things to come, by a greater and more perfect tabernacle, not made with hands, that is to say, not of this building; Neither by the blood of goats and calves, but by his own blood he entered in once into the holy place, having obtained eternal redemption for us. For if the blood of bulls and of goats, and the ashes of an heifer sprinkling the unclean, sanctifieth to the purifying of the flesh: How much more shall the blood of Christ, who through the eternal Spirit offered himself without spot to God, purge your conscience from dead works to serve the living God? And for this cause he is the mediator of the new testament, that by means of death, for the redemption of the transgressions that were under the first testament, they which are called might receive the promise of eternal inheritance. Hebrews 9:11-15 (KJV)
Again it is the ceremonial law and its aspects that are done away and were vanishing at the time of the writing of Hebrews. They completely vanish at the destruction of the temple in 70ad as Gods judgement comes on Israel by the hands of the Romans.
For Christ is not entered into the holy places made with hands, which are the figures of the true; but into heaven itself, now to appear in the presence of God for us: Nor yet that he should offer himself often, as the high priest entereth into the holy place every year with blood of others; For then must he often have suffered since the foundation of the world: but now once in the end of the world hath he appeared to put away sin by the sacrifice of himself. Hebrews 9:24-26 (KJV)
The writer of Hebrews continues in Hebrews 10 reiterating his point that the ceremonial law was a shadow of good things to come, which in itself shows that even the giving of the ceremonial law was gracious, but was not the very image of what was to come, which was Christ. The ceremonial system was the Restorative law, which was a constant reminder of their sin and their need for a Savior, and that the promised Messiah would come one day.
For the law having a shadow of good things to come, and not the very image of the things, can never with those sacrifices which they offered year by year continually make the comers thereunto perfect. For then would they not have ceased to be offered? because that the worshippers once purged should have had no more conscience of sins. But in those sacrifices there is a remembrance again made of sins every year. For it is not possible that the blood of bulls and of goats should take away sins. Hebrews 10:1-4 (KJV)
Then after giving those in the covenant, the glorious explanation of the New Covenant administration of Grace, he goes on to warn them that they hold fast their profession of faith, not wavering, but instead exhort and provoke one another to good works (see Ephesians 2:8-10, saved unto good works). He compares the same issue of falling away in the old administration to the new and says of how much more will the punishment be for those who trample the Son of God and the blood of the covenant. The Lord shall judge HIS PEOPLE.
Let us hold fast the profession of our faith without wavering; (for he is faithful that promised;) And let us consider one another to provoke unto love and to good works: Not forsaking the assembling of ourselves together, as the manner of some is; but exhorting one another: and so much the more, as ye see the day approaching. For if we sin wilfully after that we have received the knowledge of the truth, there remaineth no more sacrifice for sins, But a certain fearful looking for of judgment and fiery indignation, which shall devour the adversaries. He that despised Moses’ law died without mercy under two or three witnesses: Of how much sorer punishment, suppose ye, shall he be thought worthy, who hath trodden under foot the Son of God, and hath counted the blood of the covenant, wherewith he was sanctified, an unholy thing, and hath done despite unto the Spirit of grace? For we know him that hath said, Vengeance belongeth unto me, I will recompense, saith the Lord. And again, The Lord shall judge his people. It is a fearful thing to fall into the hands of the living God. Hebrews 10:23-31 (KJV)
Chapter 11 then gives application of Holy Spirit wrought works by faith in the Older Testament saints and shows that they looked forward to the promised Messiah, while in time not yet come. Making the New Covenant a better covenant administration because it is finished having brought together those of the Older administration and those of the New by the blood of Christ.
And these all, having obtained a good report through faith, received not the promise: God having provided some better thing for us, that they without us should not be made perfect. Hebrews 11:39,40 (KJV)
He exhorts those in the covenant to follow the lead of their forefathers in the older testament administration and move into sanctification because we have been justified.
Wherefore seeing we also are compassed about with so great a cloud of witnesses, let us lay aside every weight, and the sin which doth so easily beset us, and let us run with patience the race that is set before us, Looking unto Jesus the author and finisher of our faith. Hebrews 12:1, 2 (KJV)