There is no New Testament prescription for the office of Priest that is in keeping with the Roman Catholic, or Orthodox churches. To the contrary, the teaching is that there is only one Who fulfilled the office of Priest, it is the Lord Jesus Christ. The New Testament priesthood is made up of all Christians. It isn’t an office reserved for individual men. Those Old Testament Priests were of the tribe of Levi, and had very specific, God ordained duties to perform in the tabernacle, and later in the temple. All of those duties were pointing forward to the incarnate Lord’s sacrifice as the spotless Passover lamb. There is no efficacious works for a human priest to perform that have not been perfectly completed by Christ during the crucifixion, death, burial, and resurrection.

14 Therefore, since we have a great high priest who has passed through the heavens, Jesus the Son of God, let us take hold of our confession. 15 For we do not have a high priest who cannot sympathize with our weaknesses, but One who has been tempted in all things like we are, yet without sin. 16 Therefore let us draw near with confidence to the throne of grace, so that we may receive mercy and find grace to help in time of need.
​1 For every high priest taken from among men is appointed on behalf of men in things pertaining to God, in order to offer both gifts and sacrifices for sins, 2 being able to deal gently with the ignorant and misguided, since he himself also is beset with weakness; 3 and because of it, he is obligated, just as for the people, to also offer sacrifices for sins in the same way for himself. 4 And no one takes this honor to himself, but receives it when he is called by God, even as Aaron was.
5 In this way also Christ did not glorify Himself to become a high priest, but He who said to Him,
“YOU ARE MY SON,
TODAY I HAVE BEGOTTEN YOU”;
6 just as He says also in another passage,
“YOU ARE A PRIEST FOREVER
ACCORDING TO THE ORDER OF MELCHIZEDEK.”
7 He, in the days of His flesh, offered up both prayers and supplications with loud crying and tears to the One able to save Him from death, and He was heard because of His reverence. 8 Although He was a Son, He learned obedience from the things which He suffered. 9 And having been made perfect, He became to all those who obey Him the source of eternal salvation, 10 being designated by God as a high priest according to the order of Melchizedek. Hebrews 4:14 – 5:10 (LSB Strong’s)

23 And the former priests, on the one hand, existed in greater numbers because they were prevented by death from continuing, 24 but Jesus, on the other hand, because He continues forever, holds His priesthood permanently. 25 Therefore He is able also to save forever those who draw near to God through Him, since He always lives to make intercession for them.
26 For it was fitting for us to have such a high priest, holy, innocent, undefiled, separated from sinners and exalted above the heavens; 27 who does not need daily, like those high priests, to offer up sacrifices, first for His own sins and then for the sins of the people, because this He did once for all when He offered up Himself. 28 For the Law appoints men as high priests who are weak, but the word of the oath, which came after the Law, appoints a Son, who has been made perfect forever.
Jesus, High Priest of a New Covenant
​1 Now the main point in what is being said is this: we have such a high priest, who sat down at the right hand of the throne of the Majesty in the heavens, 2 a minister in the holy places and in the true tabernacle, which the Lord pitched, not man. 3 For every high priest is appointed to offer both gifts and sacrifices; so it is necessary that this high priest also have something to offer. 4 Now if He were on earth, He would not be a priest at all, since there are those who offer the gifts according to the Law; 5 who serve a copy and shadow of the heavenly things, just as Moses was warned by God when he was about to erect the tabernacle; for, “SEE,” He says, “THAT YOU MAKE all things ACCORDING TO THE PATTERN WHICH WAS SHOWN YOU ON THE MOUNTAIN.” 6 But now He has obtained a more excellent ministry, by as much as He is also the mediator of a better covenant, which has been enacted on better promises. Hebrews 7:23 – 8:6 (LSB Strong’s)

5 you also, as living stones, are being built up as a spiritual house for a holy priesthood, to offer up spiritual sacrifices acceptable to God through Jesus Christ. 6 For this is contained in Scripture:
“BEHOLD, I LAY IN ZION A CHOICE STONE, A PRECIOUS CORNER stone,
AND HE WHO BELIEVES UPON HIM WILL NOT BE PUT TO SHAME.”
7 This precious value, then, is for you who believe; but for those who disbelieve,
“THE STONE WHICH THE BUILDERS REJECTED,
THIS BECAME THE CHIEF CORNER stone,”
8 and,
“A STONE OF STUMBLING AND A ROCK OF OFFENSE.”
They stumble because they are disobedient to the word, and to this stumbling they were also appointed.
9 But you are A CHOSEN FAMILY, A royal PRIESTHOOD, A HOLY NATION, A PEOPLE FOR God’s OWN POSSESSION, so that you may proclaim the excellencies of Him who has called you out of darkness into His marvelous light; 10 for you once were NOT A PEOPLE, but now you are THE PEOPLE OF GOD; you had NOT RECEIVED MERCY, but now you have RECEIVED MERCY. 1 Peter 2:5-10 (LSB Strong’s)

5 For there is one God, and one mediator also between God and men, the man Christ Jesus, 6 who gave Himself as a ransom for all, the witness for this proper time. 7 For this I was appointed a preacher and an apostle (I am telling the truth, I am not lying) as a teacher of the Gentiles in faith and truth. 1 Timothy 2:5-7 (LSB Strong’s)