One question, what do you mean by the New Covenant is the New Priesthood?
According to Scriptures God's "LAWS" didn't change in His Promise of a New Covenant. Only the manner in which God's Laws are to be administered, and the manner in which transgressions of God's Laws are forgiven. You can read this for yourself in Jer. 31.
According to Scriptures God made a Covenant with the Children of Israel.
Ex. 19:
5 Now therefore, if ye will obey my voice indeed, and keep my covenant, then ye shall be a peculiar treasure unto me above all people: for all the earth is mine: 6 And ye shall be unto me a kingdom of priests, and an holy nation. These are the words which thou shalt speak unto the children of Israel.
God made this same promise to Abraham.
Gen. 17:
1 And when Abram was ninety years old and nine, the LORD appeared to Abram, and said unto him, I am the Almighty God; walk before me, and be thou perfect. 2 And I will make my covenant between me and thee, and will multiply thee exceedingly.
Abraham was Faithful to God as HE explains to Abraham's son.
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; 5 Because that Abraham obeyed my voice, and kept my charge, my commandments, my statutes, and my laws.
But the Children of Israel didn't do the works of Abraham, and "Transgressed God's Commandments", breaking the Covenant God made with them.
This prompted God to destroy them because by them HIS name was blasphemed among the nations.
Ex. 32:
9 And the LORD said unto Moses, I have seen this people, and, behold, it is a stiffnecked people: 10 Now therefore let me alone, that my wrath may wax hot against them, and that I may consume them: and I will make of thee a great nation.
So did God destroy them, and continue with the "children of Moses"?
No, Moses stood between God and the People and pleaded for their life, and God relented.
30 And it came to pass on the morrow, that Moses said unto the people, Ye have sinned a great sin: and now I will go up unto the LORD; peradventure I shall make an atonement for your sin. 31 And Moses returned unto the LORD, and said, Oh, this people have sinned a great sin, and have made them gods of gold. 32 Yet now, if thou wilt forgive their sin--; and if not, blot me, I pray thee, out of thy book which thou hast written.
Remember, there is no Covenant which exists between God and these people at this time. The Tables of Stone, shattered into pieces, and the Covenant God made with them broken.
Moses went to God and sought
another Covenant. The one they had and broke contained no sacrificial "Works" for atonement. As it is written.
Jer. 22:
22 For I spake not unto your fathers, nor commanded them in the day that I brought them out of the land of Egypt, concerning burnt offerings or sacrifices: 23 But this thing commanded I them, saying, Obey my voice, and I will be your God, and ye shall be my people: and walk ye in all the ways that I have commanded you, that it may be well unto you.
This is the same Covenant God made with Abraham.
So this begs the Question, "where did the "LAWS" concerning burnt offerings and sacrifices
for Sin come from? Paul tells us in Galatians 3 that it was "ADDED"
because of Transgressions, "Til the seed should come".
So Moses went up the 2nd time to God and obtained another Covenant.
Ex. 34:
1 And the LORD said unto Moses, Hew thee two tables of stone like unto the first: and I will write upon these tables the words that were in the first tables, which thou brakest.
So the LAW stayed the same, but God "ADDED" Sacrificial "Works" to provide for forgiveness which didn't exist in the Covenant God made with Abraham or his Children in Egypt in the day HE led them out.
These "works" were part of the Priesthood "After the Order of Aaron", AKA, the Levitical Priesthood. It dealt with Justification/forgiveness of sins and only a man from the Tribe of Levi could partake of this Priesthood. (Leviticus 4) Hebrews 7-10 describe this Biblical Truth very well.
It was this Priesthood Law and its duties concerning the manner in which God's Laws were administered, and sins are forgiven, that were prophesied to change. And of course, it was temporary in its creation. As we can surely agree that God knew His Prophesied Priest, the Messiah, would come from the Tribe of Judah, and not Levi when He gave Levi His Priesthood Covenant. (Heb. 7:11-14)
We no longer go to the Levite Priest, who sits in Moses Seat, to hear the word of God because God has delivered His Oracles into our own home, into our own mind. We no longer are required to take a goat to the Levite Priest and kill it, so he can take the blood and partake in sacrificial "works of the Law" for remission of sins. The Christ of the Bible has shed HIS blood to atone for the sins of the repentant once and for all. But God's definition of Sin never changed.
This understanding is based on Scriptures and as is the case throughout known history, the religions of this world we are born into, do not reflect the truth of Scriptures. That is why Jesus and His Chosen Apostles warned of the philosophy's doctrines and traditions of men "Who come in Christ's Name".
Do the study in the confines of your own home, apart from teachings of this world's religions, and you will find the same as I did.