The first priest mentioned in the Bible is Melchisedek, who was also king of Salem.

And Melchizedek king of Salem brought forth bread and wine: and he was the priest of El-Elyon. And he blessed him, and said, Blessed be Abram of El-Elyon, possessor of heaven and earth: Genesis 14:18-19

Other than this account, Melchizedek (Melchisedec) is mentioned only in Psalms 110:4 and Hebrews 5-7, so we don't know a lot about him.

Next, are mentioned a few Egyptian priests, then Moses' father in law, Jethro, a priest of Midian.

Finally, Yahweh's priesthood was instituted with Moses' brother, Aaron and the tribe of Levi (Levites).

Some of these priests served Yahweh, some did not. By the time of the end of the prophets, the priesthood was exceedingly corrupt.

"And so then, O priests, this command is for you: If you will not listen, and if you will not take it to heart to give glory to my name," says Yahweh of hosts, "then I will send the curse on you, and I will curse your blessings; moreover I have already cursed them because you are not taking it to heart. Malachi 2:1-2

It was time for a better priesthood and a better priest.

יהוה [Yahweh, our god] said unto my foundation [the son], Sit thou at my right hand, until I make thine enemies thy footstool. יהוה [Yahweh] shall send the rod of thy strength out of Zion: rule thou in the midst of thine enemies. Thy people shall be willing in the day of thy power, in the beauties of holiness from the womb of the morning: thou hast the dew of thy youth. יהוה [Yahweh] hath sworn, and will not repent, Thou art a priest for ever after the order of Melchizedek. יהוה [Yahweh Messiah] at thy right hand shall strike through kings in the day of his wrath. Psalms 110:1-5 (see explanation here)

This Psalms is cited 22 times in the New Testament. In all cases, it interprets the meaning to refer to Yahushua, the Messiah, priest or king. This Psalms is a prophecy of the coming better priest after the order of Melchizedek.

Yahushua challenged the Pharisees with this text:

While the Pharisees were gathered together, Yahushua asked them, Saying, What think ye of the Messiah? whose son is he? They say unto him, The Son of David. He saith unto them, How then doth David in spirit call him [his foundation], saying, יהוה [Yahweh] said unto my [foundation], Sit thou on my right hand, till I make thine enemies thy footstool? If David then call him his [foundation], how is he his son? Matthew 22:41-45 (see explanation here)

The Jews knew that the Messiah would come from the seed of David, therefore He would be a Son of David. They also knew that this Psalms was a Messianic prophecy (we know that because they didn't deny or challenge Yahushua's inference).

Jehovah said to my foundation....

"My foundation" here is the Messiah. If the Messiah were David's son why did David here refer to him as "my foundation" (David's foundational base, his ancestor)? (see explanation here)

This is confirmed in Isaiah and Revelation:

I Yahushua [Jesus] have sent mine angel to testify unto you these things in the assemblies. I am the root [foundation] and the offspring [son] of David, and the bright and morning star. Revelation 22:16

And in that day there shall be a root of Jesse [David's father], which shall stand for an ensign of the people; to it shall the Gentiles seek: and his rest shall be glorious. Isaiah 11:10

This prophecy of David says that the Messiah would be a high priest for ever after the order of Melchizedek. This is a better priesthood than that of Aaron. Those priests die. They also had to constantly go into the temple ministering sacrifices.

The better priest lived for ever, therefore unchangeable, and had to go in only once.

Who needeth not daily, as those high priests, to offer up sacrifice, first for his own sins, and then for the people's: for this he did once, when he offered up himself. Hebrews 7:27

If the Father hasn't sent His Messiah yet, if Yahushua, seed of the woman, isn't the Messiah, where is Yahweh's priest today? It isn't the pope, it isn't any protestant minister, it isn't any rabbi. Where is your priest?

Finally, we, the elect of Yahweh, will be made priests and kings to rule with Him.

And hast made us unto our Elohim kings and priests: and we shall reign on the earth. Revelation 5:10