The New covenant is this:
Heb 8:10 For this is the covenant that I will make with the house of Israel after those days, saith the Lord; I will put my laws into their mind, and write them in their hearts: and I will be to them a God, and they shall be to me a people:
Heb 8:11 And they shall not teach every man his neighbour, and every man his brother, saying, Know the Lord: for all shall know me, from the least to the greatest.
Heb 8:12 For I will be merciful to their unrighteousness, and their sins and their iniquities will I remember no more.
Heb 8:13 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.
notice that the new covenant is to write Gods laws on our hearts and in our minds. None the less this Covenant is not new as many of us understand new.
God made a covenant with Israel and they broke it and thus it faded away. the new covenant is a renewing of the old. how so you ask?
remember that a covenant says if you obey I will.... and if you break then this will happen....
when a covenant is broken then it becomes obsolete. thus in the mercy of God almighty He renews that same covenant but it is new in that it is drawn up again. notice the old testament scripture to Israel.
Jer 31:31 Behold, the days come, saith the LORD, that I will make a new covenant with the house of Israel, and with the house of Judah:
Jer 31:32 Not according to the covenant that I made with their fathers in the day that I took them by the hand to bring them out of the land of Egypt; which my covenant they brake, although I was an husband unto them, saith the LORD:
Jer 31:33 But this shall be the covenant that I will make with the house of Israel; After those days, saith the LORD, I will put my law in their inward parts, and write it in their hearts; and will be their God, and they shall be my people.
Jer 31:34 And they shall teach no more every man his neighbour, and every man his brother, saying, Know the LORD: for they shall all know me, from the least of them unto the greatest of them, saith the LORD: for I will forgive their iniquity, and I will remember their sin no more.
This has always been the case with God. lets take a look at the covenant given to Abraham
Gen 17:4 As for me, behold, my covenant is with thee, and thou shalt be a father of many nations.
The essence of the covenant/promise with Abraham was to make nations of Him.
why did God chose Abraham?
Answer: Gen 26:4 And I will make thy seed to multiply as the stars of heaven, and will give unto thy seed all these countries; and in thy seed shall all the nations of the earth be blessed;
Gen 26:5 Because that Abraham obeyed my voice, and kept my charge, my commandments, my statutes, and my laws.
because Abraham obeyed Gods laws, commandments and statutes.
Why did God free Israel from Egypt?
Answer: Exo 2:24 And God heard their groaning, and God remembered his covenant with Abraham, with Isaac, and with Jacob.
Exo 2:25 And God looked upon the children of Israel, and God had respect unto them.
It was the covenant with Abraham that caused Got to save Israel. notice that the covenant was with Abraham and Isaac and Jacob and now Israel. all in the same line all the same covenant.
Notice again:
Exo 6:3 And I appeared unto Abraham, unto Isaac, and unto Jacob, by the name of God Almighty, but by my name JEHOVAH was I not known to them.
Exo 6:4 And I have also established my covenant with them, to give them the land of Canaan, the land of their pilgrimage, wherein they were strangers.
Exo 6:5 And I have also heard the groaning of the children of Israel, whom the Egyptians keep in bondage; and I have remembered my covenant.
this is not a new covenant but the same one God gave to Abraham.
What was the covenant with Israel that was the same as with Abraham?
Exo 34:28 And he was there with the LORD forty days and forty nights; he did neither eat bread, nor drink water. And he wrote upon the tables the words of the covenant, the ten commandments.
notice that the covenant is the ten commandments. remember that the blessings and promises came to Abraham why?
Gen 26:5 Because that Abraham obeyed my voice, and kept my charge, my commandments, my statutes, and my laws.
The ten commandments were not new with Israel. the promise was and has always been in condition to obedience to Gods law.
Remember that a covenant has blessings or rewards if you keep it and curses or punishments if you do not. In Abraham case the blessings was to become a nation and to live in the land God was going to give them. what was this land?
Heb 11:9 By faith he sojourned in the land of promise, as in a strange country, dwelling in tabernacles with Isaac and Jacob, the heirs with him of the same promise:
Heb 11:10 For he looked for a city which hath foundations, whose builder and maker is God.
notice the promise even Abraham understood to be the heavenly city and not one of earth.
Heb 11:39 And these all, having obtained a good report through faith, received not the promise:
Heb 11:40 God having provided some better thing for us, that they without us should not be made perfect.
notice we are told that they have not yet received it not until we are made perfect with them. In other words we are also heirs of the same promise the same covenant given to Abraham and passed to Israel.
Gal 3:29 And if ye be Christ's, then are ye Abraham's seed, and heirs according to the promise.
Notice we are heirs of the same promise the same covenant.
This is why the new covenant is about the law of God being written in our heart and in our mind. thus if we obey Gods commandments then we are heirs of the same promise. the covenant has always been the same promise based on the same condition. there is much more to say about this but this is sufficient for now.
blessings