Albert Barnes Commentary Leviticus 8:13

"And Moses brought Aaron`s sons, and clothed them with coats, and girded them with girdles, and bound head-tires upon them; as Jehovah commanded Moses." — Leviticus 8:13 (ASV)

Aaron’s sons - The common priests. Nothing is said here, or in (Exodus 29:7–9), of the anointing of the common priests, though it is expressly commanded in (Exodus 28:41); (Exodus 40:15), and is evidently implied as a fact in (Leviticus 7:36); (Leviticus 10:7); (Numbers 3:3). It would seem that the anointing of the common priests consisted in some rite common to them and the high priest (Exodus 40:15), and this was the sprinkling mentioned in (Leviticus 8:30). Compare further (Leviticus 10:7) with (Leviticus 21:12).