The author isn't just talking about a different priest; he's talking about a completely different order. Why is the contrast between Aaron and Melchizedek so significant?
The entire point of this passage is to elevate Christ's priesthood above the Levitical one. The question posed in verse 11 is rhetorical: 'What further need was there for another priest to arise after the order of Melchizedek, rather than one named after the order of Aaron?' The implication is clear: there was a need. Melchizedek represents a priesthood that is not bound by lineage (he had no recorded father or mother, and his genealogy wasn't traced through Levi), has an unending life, and is even greater than Abraham (and thus greater than Levi). Aaron, on the other hand, represents a priesthood tied to a specific tribe, limited by human lifespan, and subordinate. By contrasting these two, the writer sets the stage to show that Jesus, our great High Priest, belongs to this superior, eternal order of Melchizedek, fulfilling what the Aaronic priesthood could only foreshadow.