Old Covenant / New Covenant (Jer. 31:31,34,Heb. 8:5-13)

Consequently, a covenant sign that focused on physical descent through the male line was no longer appropriate. A new sign of the covenant was needed—one that all people, whether Jew or Gentile, male or female, could receive. As we have seen, water baptism was instituted by Jesus as the new sign of entrance into the community of faith. Essentially, then, baptism replaced circumcision.

The Second Pillar of the Law of the New Covenant

There are no grounds for using the Old Covenant to reinforce the New Covenant.

The Abrahamic Covenant, A Promise of a New Covenant

The days are coming, says the Lord,
when I will make a new covenant with the house of Israel
and the house of Judah.
It will not be like the covenant I made with their fathers:
the day I took them by the hand
to lead them forth from the land of Egypt.
But this is the covenant which I will make
with the house of Israel after those days, says the Lord.
I will place my law within them, and write it upon their hearts;
I will be their God, and they shall be my people.
No longer will they have need to teach their friends and relatives
how to know the Lord.
All, from least to greatest, shall know me, says the Lord.
The word of the Lord.

The Pillar Laws of the New Covenant by Gary Amirault

Therefore, it should not be unreasonable to suspect there would be a new law which would accommodate moving from the types and shadows of the heavenly realm to the heavenly realm itself. The law of the New Covenant does not require one to stone their rebellious children. It does not require one to sleep with his brother’s wife if the brother died and the wife did not bear an heir yet. The New Covenant does not require many of the things which the Mosaic Law required. The name of this law is “the Law of the Spirit of the Life in Christ Jesus.”

The New Covenant does not have a ruling priesthood which must offer sacrifices daily.
Not one tithe or offering was ever used to evangelize other nations in the Old Covenant.

Old Testament vs. New Testament - What are the …

Please understand the "Law" in this passage refers to the Mosaic Law. The Mosaic Law is the New Covenant. Please look at these two commandments. Have you not heard them a thousand times in the context of the Christian message? And yet, as we just saw, the Scriptures make it abundantly clear that no one will be justified according to the Law of Moses. Striving to meet these two single commandments, the summary of the Mosaic Law will not justify one, yet we continue to stand upon these two commandments as being the foundation of the New Covenant. Please understand, these two commandments could only be fulfilled by one man, the Man, Christ Jesus. Please hear this. This is vitally important. One cannot deeply love someone unless they know them intimately. Of all the men and women born into this world since Adam, only Jesus Christ could lay claim to this intimacy. He was the only Man who came down from the Father. Jesus could say He loved the Father because He intimately knew Him as Father. Moses, not born of God, could not make that claim. No one born under the Law of Moses, except Jeus the Messiah, could make that claim.

We see then, that the New Covenant was the fulfillment of God’s promise to Abraham.  (Gal. 3:8,9)

The Pillar Laws of the New Covenant - Tentmaker

NIV: He has made us competent as ministers of a new covenant -- not of the letter but of the Spirit; for the letter kills, but the Spirit gives life.

NIV: By calling this covenant

Old vs New Covenant | Armchair Theologian

NIV: Now the first covenant had regulations for worship and also an earthly sanctuary. A tabernacle was set up. In the firs room were the lampstand, the table and the consecrated bread; this was called the Holy Place . Behind the second curtain was a room called the Most Holy Place , which had the golden altar of incense and the gold-covered ark of the covenant. This ark contained the gold jar of manna, Aaron's rod that had budded, and the stone tablets of the covenant. Above the ark were the cherubim of the Glory, over-shadowing the place of atonement. But we cannot discuss these things in detail now. When everything had been arranged like this, the priests entered regularly into the outer room to carry on their ministry. But only the high priest entered the inner room, and that only once a year, and never without blood, which he offered for himself and for the sins the people had committed in ignorance. The Holy Spirit was showing by this that the way into the Most Holy Place had not yet been disclosed as long as the first tabernacle was still standing. This is an illustration for the present time, indicating that the gifts and sacrifices being offered were not able to clear the conscience of the worshiper. They are only a matter of food and drink and various ceremonial washings - external regulations applying until the time of the new order. When Christ came as high priest of the good things that are already here, he went through the greater and more perfect tabernacle that is not man-made, that is to say, not a part of this creation. He did not enter by means of the blood of goats and calves, but he entered the Most Holy Place once for all by his own blood, having obtained eternal redemption. The blood of goats and bulls and the ashes of a heifer sprinkled on those who are ceremonially unclean sanctify them so that they are outwardly clean. How much more, then, will the blood of Christ, who through the eternal Spirit offered himself unblemished to God, cleanse our consciences from acts that lead to death, so that we may serve the living God! For this reason Christ is the mediator of a new covenant, that those who are called may receive the promised eternal inheritance -- now that he has died as a ransom to set them free from the sins committed under the first covenant. In the case of a will, it is necessary to prove the death of the one who made it, because a will is in force only when somebody has died; it never takes effect while the one who made it is living. This is why even the first covenant was not put into effect without blood. When Moses had proclaimed every commandment of the law to all the people, he took the blood of calves, together with water, scarlet wool and branches of hyssop, and sprinkled the scroll and all the people. He said, "This is the blood of the covenant, which God has commanded you to keep." In the same way, he sprinkled with the blood both the tabernacle and everything used in its ceremonies. In fact, the law requires that nearly everything be cleansed with blood, and without the shedding of blood there is no forgiveness. It was necessary, then, for the copies of the heavenly things to be purified with these sacrifices, but the heavenly things themselves with better sacrifices than these. For Christ did not enter a man-made sanctuary that was only a copy of the true one; he entered heaven itself, now to appear for us in God's presence. Nor did he enter heaven to offer himself again and again, the way the high priest enters the Most Holy Place every year with blood that is not his own. Then Christ would have had to suffer many times since the creation of the world. But now he has appeared once for all at the end of the ages to do away with sin by the sacrifice of himself. Just as man is destined to die once, and after that to face judgment, so Christ was sacrificed once to take away the sins of many people; and he will appear a second time, not to bear sin, but to bring salvation to those who are waiting for him.