Generally the priests were not allowed to eat from it (see Leviticus 4:16, Leviticus 6:30), as they were included in the people. This time it is different, apparently because the offering is not brought for an actual sin of the people (see Leviticus 4:13).
17 “Why have you not eaten the sin offering in the place of the sanctuary, since it is a thing most holy and has been given to you that you may bear the iniquity of the congregation, to make atonement for them before the LORD?