Leviticus 9:7

And Moses said unto Aaron
This is only observed to show, that as Aaron did not take upon him this office of himself, but was called unto it, and invested with it, by the appointment of God, so neither did he enter upon it but through the call of God by Moses, in the sight of the congregation:

go unto the altar, and offer thy sin [offering], and thy burnt
offering;
the young calf and ram:

and make an atonement for thyself and for the people;
first for himself, and then for the people; for, as Aben Ezra says, a man cannot atone for another until he is pure from all sin; which is a character only to be found in Christ, our great High Priest, and so a proper person to atone for and take away the sins of others: hence the priests under the law, with their sacrifices, could never take away sin really, only typically; and this shows the imperfection of the Levitical priesthood, that the priests of that order were obliged to offer first for their own sins; this our high priest, of another order, needed not to do; see ( Hebrews 7:27 Hebrews 7:28 )

and offer the offering of the people, and make atonement for them;
typical of the true and full atonement made by Christ, when he offered himself without spot to God:

as the Lord commanded;
Aaron to do, and as he commanded Christ, his Son and our surety, the antitype of Aaron, ( John 10:18 ) ( 14:31 ) .