Albert Barnes Commentary Leviticus 7:8

"And the priest that offereth any man`s burnt-offering, even the priest shall have to himself the skin of the burnt-offering which he hath offered." — Leviticus 7:8 (ASV)

The skin of the burnt offering: It is most likely that the skins of the sin-offering and the trespass-offering also became the portion of the officiating priest.