The order of the Melchizedek priesthood is a prominent theme in the NT epistle of Hebrews (5:6, 10; 6:20; 7:1-28), even though the inspired writer(s) acknowledge the doctrine is “hard to explain” (Heb. 5:10-11). The teaching begins with the historical account of Melchizedek, the king of Salem (Heb. 7:1-10; see Gen. 14:17-20; Psa. 110:4). His name means “king of righteousness,” and “Salem” (or shalom) means “peace” (Heb. 7:1-2). Righteousness and peace are also qualities of the messianic king and his kingdom (cf. Heb. 1:8; Psa. 72:7; Isa. 9:6-7).
Melchizedek was “priest of the Most High God,” long before the Levitical priesthood of the Israelites. Some form of mediatorial priesthood seems to have existed from the earliest times, the duties of which were discharged by those who occupied positions of leadership.1 Abraham gave Melchizedek “a tenth of all [the spoils of his victory],” following the rescue of Lot and after Melchizedek had blessed him (Heb. 7:1-2a; cf. Gen. 14:14-20).
Melchizedek is said to have been without father, mother, genealogy, beginning or end (Heb. 7:3a), which must be understood with respect to his priesthood. Under the Law of Moses the office of priest was determined by ancestry (cf. Deut. 18:1-8). Melchizedek’s priesthood was conferred directly from God, perhaps based on personal credentials, but was not inherited from his parents or according to genealogical descent. The Levitical priesthood (through Aaron’s family) was passed on from generation to generation, so there was a beginning and an end in conjunction with the lifespan of each priest (cf. Heb. 7:23; Num. 20:24-29). Melchizedek’s priesthood was not inherited by a predecessor or passed on to a successor, thus there was no beginning or end in the sense of succession.
Melchizedek was “made like the Son of God” in that his priesthood abides “continually” (NKJ) or “perpetually” (NAS) or “forever” (NIV) (Heb. 7:3b). The Melchizedek order of priesthood is superior to the Levitical order of priesthood (Heb. 7:4-10) for the following reasons. First, Melchizedek received tithes from Abraham (vv. 4-6) – the acknowledged father of all Jews. Second, Melchizedek (the greater) blessed Abraham (the lesser) (v. 7). Third, mortal (lit. “dying”) men (i.e., Levitical priests) receive tithes “here” (presently–at the time of writing), but they eventually die and are succeeded, whereas Melchizedek received tithes “there” (in the past) but he “lives on” (v. 8); as far as historical documentation, his death is unrecorded and he lives on in scripture, and he lives on in the sense that his priesthood has no end (cf. v. 3). Finally, Levi himself, in proxy through his great-grandfather Abraham, paid ties to Melchizedek (vv. 9-10).
The rest of the chapter addresses the importance of the new priesthood (Heb. 7:11-28), and the main point is that Jesus is now our great High Priest and therefore superior to the old-covenant system of the Jews (Heb. 8:1–10:23). As a descendent of Judah rather than Levi he could not serve as high priest under the old system. But since his priesthood is according to a different order, viz. the order of Melchizedek, his role is divinely authorized and scripturally justified for the reasons just given.
-- Kevin L. Moore
1 Cain and Abel made offerings to the Lord (Gen. 4:3-4; Heb. 11:4). Noah “built an altar to the LORD . . . and offered burnt offerings on the altar” (Gen. 8:20). Job offered burnt offerings for his children (Job 1:5). Abraham built an altar and offered a ram for a burnt offering (Gen. 22:9-13; cf. 12:7, 8; 13:4, 18). Melchizedek was “the priest of God Most High” (Gen. 14:18-20; Heb. 7:1-10). Jethro was “the priest of Midian (Ex. 2:16; 3:1). Following their deliverance from exile in Egypt, a priesthood limited to Aaron and his family was established among Israel (Ex. 28 ff.).
Image credit: https://3wisdoms.com/2020/01/15/melchizedek-and-the-magi/