Albert Barnes Commentary Leviticus 4:3

"if the anointed priest shall sin so as to bring guilt on the people, then let him offer for his sin, which he hath sinned, a young bullock without blemish unto Jehovah for a sin-offering." — Leviticus 4:3 (ASV)

The priest that is anointed – that is, the high priest. (Leviticus 21:10; Exodus 29:7). On the anointing of the other priests, see the note at Leviticus 8:13.

The graduation of the sin-offerings is remarkable. It might seem that the distinction applied more pointedly to each individual according to his rank and consequent responsibility .

According to the sin of the people – Rather, to bring guilt on the people. The whole nation is affected by every transgression of its representative.