Excerpts from A.W. Pink:
Hebrews 7:15 Melchizedek is there as a type of Christ, king of Salem, i.e., Prince of Peace.
18 And
Melchizedek king of Salem brought forth bread and wine: and
he was priest of God Most High. Gen 14
15 And
what we say is yet more abundantly evident, if
after the likeness of Melchizedek there ariseth another priest, Heb 7
"
“But made like unto the Son of God”, or, more literally “but assimilated to the Son of God”. It is very striking to note that it is not the Son of God who was “assimilated to Melchizedek”, but vice versa. In the order of time Christ subsisted before Melchizedek; in the order of nature, Melchizedek was a priest before Christ was. The priesthood of the Son of God, ordained and appointed by the Eternal Three, was the original, and Melchizedek’s priesthood furnished the copy, and a copy given in advance is the same thing as the type. Melchizedek was “assimilated to the Son of God” as a type.
First , as priest of the most high God.
Second , as being a royal priest, possessing personal majesty and authority.
Third , as being the king of righteousness.
Fourth , as king of peace.
Fifth , as the one who “blessed Abraham”.
Sixth , as the one who received the grateful gifts of God’s people represented by Abraham.
Seventh, as not owing his priesthood to natural genealogy.
Eighth, as abiding a priest beyond the bounds of the Levitical limitations. “Abideth a priest continually” (verse 3).
Note carefully it is not that the natural life of Melchizedek had no end, but that his priestly life did not cease at the age of fifty; in other words, he continued a priest to the very end of his earthly existence, which shows he had no vicar or successor, deriving a priesthood from his. “The expression ‘abideth a priest continually’, therefore, is the equivalent to saying that he had a perpetual priesthood in contradistinction from those whose office terminated at a definite period, or whose office passed over into the hands of others” (A. Barnes)."
CHAPTER - MELCHIZEDEK (godrules.net)