When a worthy young man reaches age 18 he may receive the Melchizedek Priesthood and be ordained an elder. However, because of individual maturity, school graduation, or peer group association, a bishop may let a worthy 18-year-old remain a priest for a period of time. By age 19, all young men should be affiliated with the elders quorum as elders or prospective elders.
Adult male converts should receive the Aaronic Priesthood and be ordained priests. There is no specific time they must wait before receiving the Melchizedek Priesthood, though they first should serve as a priest and demonstrate their worthiness.
Melchizedek Priesthood Handbook, p. 11.