According to Scripture (the letter to the Hebrews), it is Jesus Himself who is a priest like Melchizedek.
The original Melchizedek was both king of the small city-state of Salem (which later because Jerusalem) and the high priest of its religion. (They worshipped El Elyon, God Most High, which title Abraham recognized as another name for YHWH.)
There is only ever one "priest in the order of Melchizedek" at a time. There can't be more than one. Some scholars suggest that Melchizedek was actually a pre-incarnation appearance of Jesus.
Here's what Hebrews chapter 7 says:
7 This Melchizedek was king of Salem and priest of God Most High. He
met Abraham returning from the defeat of the kings and blessed him, 2
and Abraham gave him a tenth of everything. First, the name
Melchizedek means “king of righteousness”; then also, “king of Salem”
means “king of peace.” 3 Without father or mother, without genealogy,
without beginning of days or end of life, resembling the Son of God,
he remains a priest forever.
4 Just think how great he was: Even the patriarch Abraham gave him a
tenth of the plunder! 5 Now the law requires the descendants of Levi
who become priests to collect a tenth from the people—that is, from
their fellow Israelites—even though they also are descended from
Abraham. 6 This man, however, did not trace his descent from Levi, yet
he collected a tenth from Abraham and blessed him who had the
promises. 7 And without doubt the lesser is blessed by the greater. 8
In the one case, the tenth is collected by people who die; but in the
other case, by him who is declared to be living. 9 One might even say
that Levi, who collects the tenth, paid the tenth through Abraham, 10
because when Melchizedek met Abraham, Levi was still in the body of
his ancestor. Jesus Like Melchizedek
11 If perfection could have been attained through the Levitical
priesthood—and indeed the law given to the people established that
priesthood—why was there still need for another priest to come, one in
the order of Melchizedek, not in the order of Aaron? 12 For when the
priesthood is changed, the law must be changed also. 13 He of whom
these things are said belonged to a different tribe, and no one from
that tribe has ever served at the altar. 14 For it is clear that our
Lord descended from Judah, and in regard to that tribe Moses said
nothing about priests. 15 And what we have said is even more clear if
another priest like Melchizedek appears, 16 one who has become a
priest not on the basis of a regulation as to his ancestry but on the
basis of the power of an indestructible life. 17 For it is declared:
“You are a priest forever,
in the order of Melchizedek.”[a]
18 The former regulation is set aside because it was weak and useless
19 (for the law made nothing perfect), and a better hope is
introduced, by which we draw near to God.
20 And it was not without an oath! Others became priests without any
oath, 21 but he became a priest with an oath when God said to him:
“The Lord has sworn
and will not change his mind:
‘You are a priest forever.’”[b]
22 Because of this oath, Jesus has become the guarantor of a better
covenant.
23 Now there have been many of those priests, since death prevented
them from continuing in office; 24 but because Jesus lives forever, he
has a permanent priesthood. 25 Therefore he is able to save
completely[c] those who come to God through him, because he always
lives to intercede for them.
26 Such a high priest truly meets our need—one who is holy, blameless,
pure, set apart from sinners, exalted above the heavens. 27 Unlike the
other high priests, he does not need to offer sacrifices day after
day, first for his own sins, and then for the sins of the people. He
sacrificed for their sins once for all when he offered himself. 28 For
the law appoints as high priests men in all their weakness; but the
oath, which came after the law, appointed the Son, who has been made
perfect forever.
Sects which claim a Melchizedek priesthood for some of their clergy are talking unbiblical nonsense. Their clergy are mortal men who age and die. They are not "without beginning of days nor end of life".
So Jesus is the one and only Melchizedek-type priest, and the temporary priesthood of Aaron (which was central to the Old Covenant between God and the 12 tribes of Israel) is gone.