THE ORIGINAL COVENANT - A KINGDOM OF PRIESTS
The original covenant at Sinai in Exodus 19, continued the Patriarchal pattern of every man being a priest over his own household. It was under this priesthood which had functioned from Adam down to Noah and finally to Abraham, Isaac and Jacob, that was still current when the nation of Israel was in Egypt, although it had been dysfunctional due to the oppression of the taskmasters of Egypt.
The first instruction once they come out of Egypt was for the firstborn of all males to be consecrated to function again in their service. (Exodus 13:1-2, 12) Then He says to them once they arrive at Sinai,
"Now therefore, if you will indeed obey My voice and keep My covenant, then you shall be a special treasure unto Me above all people; for all the earth is Mine. And you shall be to Me a kingdom of priests and a holy nation." (Exodus 19:5-6)
But Israel defaulted on this covenant at the incident of the golden calf (Exodus 32) and so the Levitical system was introduced of one tribe, who was accounted worthy through their faithfulness, to do the priestly service for the whole nation. (Exodus 32:28, Numbers 3:5-14). They would no longer be a kingdom of priests, but a nation served by one of their tribes doing the priestly service. The nation as a whole lost its status and the original purpose of Yahweh God was deferred until One came who had the power to bring the covenant into effect.
THE NEW COVENANT REPEATS THE OLD
When Peter expounds on the priesthood of the new covenant, he refers back to the original covenant in Exodus 19:4-6 of them becoming a kingdom of priests. This covenant which was made with Israel before the incident of their sin with Golden Calf that broke the covenant, became effective in the new covenant (1 Peter 2:4-10).
Through the sacrifice of Yeshua the Messiah and His High Priestly service, He has made the covenant effectual so that now they are as Peter says, "His own special people", a "royal priesthood, a holy nation" (1 Peter 2:9). To have a "kingdom of priests" was, and is, His eternal purpose (Ephesians 3:11).
Into this now "chosen", "holy" nation, the Gentiles have been grafted in to become part of Israel. What was once a wild branch, has been grafted into the Olive tree, which is Israel (Romans 11:13-24). The kingdom now is comprised of Jew and Gentile which becomes one "new man" in Him, no longer Jew and Gentile but all part of the greater Israel of God. (Romans 11:11, 16-18 - Jews broken off - wild grafted in)
THE ERROR OF REPLACEMENT THEOLOGY
Replacement theology is the doctrine that the Church has replaced Israel. This presumes that the Jews have been forsaken because they did not embrace their Messiah as a nation when He came, and have therefore been cast away. But, their 'casting away' is a temporary "blindness" to admit the "Gentiles" to be grafted in that the Gentile believers might by their example, provoke the Jews to jealousy as they behold the spiritual riches they have inherited. This is all part of God's wisdom that the Gentiles/nations might be included in His purposes and that all might be saved eventually. Paul warns against the believers in the nations becoming proud and assuming that the Jews have been permanently cast away, rather than realising that it is all the providence of God and His mercy that they are included. (Romans 11:11-15, 25-33).
What Paul is actually saying, is that the restoration of all things for the completion of Yahweh God's purposes, is dependant upon the natural branches being grafted back into the olive tree again to bring it forth into the fullness of resurrection life. Believers in the nations are not a separate from Israel.
Paul taught that in the new covenant, although they are still identified separately, there is no longer Jew/Gentile as being different before God, BUT one new man - the new order of 'man' (Galatians 3:28; Coloss.3:11). The Gentile "Church" has not become a new entity BUT, according to Paul, they are - "fellow-heirs, of the same Body, and partakers of the same promise" (Ephesians 3:6)
THE LAW AND THE COVENANT
Paul takes the non-Jewish believers back to Abraham to establish the foundation of their faith in Yeshua and the promises, saying, "Now to Abraham and to his Seed were the promises made." (Galatians 3:16) Abraham is the father-figure who walked by faith with Yahweh God in the principles of His Law before the formal giving of the Law at Sinai. Abraham was chosen for this role-model because he was faithful to walk in all the principles of God's laws, precepts and commandments etc., and not apart from them (Genesis 26:4-5).
The new covenant believer is called to walk in this same faith relationship as their spiritual father who was also called out of the idolatry of the 'world' of his day, and to function under the Melchizedek priesthood.
Abraham needed to offer animal sacrifices because Yeshua had not yet come, but when He did, He was the perfect sacrifice for sin, slain once for all. Through His sacrifice, the daily sacrifices for sin became obsolete, both in the previous Patriarchal order and in the Levitical priesthood. Therein, all the ceremonial rites for the priesthood and all the laws regarding the animal sacrifices came to an end.
Those laws became obsolete, but the eternal Law of God remained the same. The Law is, after all, the standard of God's righteous nature in which man was created before he fell into sin. Yeshua said that He did not come to do away with the Law of God although He did fulfill it through His life and His sacrifice for sin (Matthew 5:17). He fulfilled the prophecies regarding Himself as the Saviour of Israel , to be that "lamb led to the slaughter" that bore the iniquity of His people (Isaiah 53:4-8; Acts 3:18), so that they would be freed from judgment.
The animal sacrificial laws were given because of man's transgression, as a ceremonial rite to impress upon the sinner the consequences of his sin and to be a means whereby he could express his faith in the promised Messiah, which they represented. All of the sacrifices pointed toward His redemption of the Adamic race.
All ceremonies and laws which were added to instruct the nation in righteousness are separate from and in addition to the eternal Law of God. In the progressive plan of man's redemption, changes have been made in the terms of the covenants which He has made with His people, but His eternal Law is unchanging. God's standards of holiness and righteousness are according to His own nature and cannot change.
Paul makes such a strong case against circumcision, in taking the believers back to Abraham before the 'law', that it would appear as if he is negating the Law of God. But this is not the case, as can be seen by comparing what he is saying with other scriptures. He was dealing with a contemporary problem caused by the Judaisers who wanted to bring the new converts under the old covenant procedures in circumcision. See Acts 15. See what Paul himself says, that the only way that we can know what sin is, was by the law.
"Therefore the law is holy, and the commandment holy, and just, and good. " (Romans 7:12)
"The law/torah of Yahweh is perfect converting the soul" (Psalm 19:7) "What shall we say then? Is the law sin? Certainly not! I would not have known sin, except through the law: for I had not known covetousness, except the law had said, you shall not covet". (Romans 7:7)
"Therefore by the deeds of the law there shall no flesh be justified in his sight; for by the law is the knowledge of sin." (Romans 3:20)
Although we are not made righteous with God by our own efforts at keeping His Law, it's holy standard gives us the yardstick with which to measure all that we do. Without it, there would be no regulation upon our behaviour, every man would be free to do what was right in his own eyes (2 Timothy 3:16).
The other function of the Law is to bring judgment, because the penalty for sin is death (Romans 6:23). Because the law brings about wrath: for where no law is, there is no transgression. (Romans 4:15)
Because the Law exposes what sin is, it also is the means whereby judgment can be justly executed.
"But we know that the Law is good if one use it lawfully, knowing this: that the law is not made for a righteous person, but for the lawless and insubordinate, for the ungodly and sinners, for the unholy and profane, for murderers ... for manslayers, for fornicators ... etc., and if there is anything that is contrary to sound doctrine, according to the glorious gospel of the blessed God which was committed to my trust." (1 Timothy 1:8-11)