John Gill Commentary Hebrews 7:13

"For he of whom these things are said belongeth to another tribe, from which no man hath given attendance at the altar." — Hebrews 7:13 (ASV)

For he of whom these things are spoken
In (Psalms 110:4) and in the type of him Melchizedek, in the preceding verses; for not Melchizedek is here meant, but the Lord Jesus Christ, as appears by what follows; the antitype of Melchizedek, the Lord our righteousness, the Prince of peace, the priest of God, that lives for ever, without father, without mother

pertains to another tribe ;
the tribe of Judah, and not the tribe of Levi:

of which no man gave attendance at the altar ;
either of burnt offering or of incense; that is, no man waited there, or took upon him and exercised the priest's office that was of the tribe of Judah: no man might lawfully do it; Uzziah, indeed, thrust himself into the priest's office, who was of that tribe, and went into the temple and burnt incense upon the altar of incense; but then he had no right to do it, and was punished for it.