Albert Barnes Commentary Leviticus 9:7

"And Moses said unto Aaron, Draw near unto the altar, and offer thy sin-offering, and thy burnt-offering, and make atonement for thyself, and for the people; and offer the oblation of the people, and make atonement for them; as Jehovah commanded." — Leviticus 9:7 (ASV)

It should be noted that Aaron offers no peace-offering for himself. It was enough that he should participate in the peace-offerings of the consecration (Leviticus 8:31), and in the two peace-offerings about to be sacrificed for the people.

His sin-offering was probably regarded not so much as a sacrifice for his own actual sins as a typical acknowledgment of his sinful nature and of his future duty to offer for his own sins and those of the People. See marginal references. The law makes men high priests who have infirmity; but the word of the oath, which was since the law, makes the Son, who is consecrated (in the margin perfected, see Leviticus 8:22 note) forevermore (Hebrews 7:28).