Succession
Succession in Hebrews 7 is the legal and theological problem the writer sets up against the Levitical priesthood: each Aaronic priest is a mortal, the office passes from father to son only because the holder dies, and the chain of succession is therefore the standing proof that the priesthood it carries cannot be perfect. The argument is built around Melchizedek, who is presented as a priest without genealogy and without succession at all.
The Mortal Chain at the Altar
The Levitical priesthood is gathered around its mortality. "They indeed of the sons of Levi who receive the priest's office have commandment to take tithes of the people according to the law" (Heb 7:5); "here men who die receive tithes" (Heb 7:8). The plurality of priests is the index of the problem: "they indeed have been made priests many in number, because by death they are hindered from staying [as priest]" (Heb 7:23). The office is transferable only because each holder is removed, and the chain itself is the symptom of weakness. "The law made nothing perfect" (Heb 7:19); "the law appoints men high priests, having infirmity" (Heb 7:28).
Melchizedek and a Priesthood Without Succession
Against that line stands Melchizedek, who is described precisely by what his record does not contain: "without father, without mother, without genealogy, having neither beginning of days nor end of life, but made like the Son of God, [he] stays a priest continually" (Heb 7:3). He has no predecessor in the text and no successor. The greatness of his rank is shown not by lineage but by the tithe Abraham pays to him: "consider how great this man was, to whom even Abraham, the patriarch, gave a tenth out of the chief spoils" (Heb 7:4); "through Abraham even Levi, who receives tithes, has paid tithes; for he was yet in the loins of his father, when Melchizedek met him" (Heb 7:9-10). Levi's whole future office is, on this argument, already inferior at its source.
A Priesthood Unchangeable
The conclusion turns the whole succession-frame inside out. Christ holds the office "not after the law of a carnal commandment, but after the power of an endless life" (Heb 7:16); the witness to him is, "You are a priest forever After the order of Melchizedek" (Heb 7:17). His sworn appointment differs from the Aaronic in kind: the Levites were made priests "without an oath; but he with an oath by him who says of him, The Lord swore and will not repent, You are a priest forever" (Heb 7:21). And because he does not die, no succession follows him: "but he, because he stays forever, has his priesthood unchangeable" (Heb 7:24). The priestly succession is closed, not by an heir, but by an heir who cannot be replaced — "a Son, perfected forever" (Heb 7:28).