‘And Moses said to Aaron, “Draw near to the altar, and offer your purification for sin offering, and your whole burnt offering, and make atonement for yourself, and for the people, and offer the oblation of the people, and make atonement for them, as Yahweh commanded.” '
Then Moses commands Aaron to carry on and for the first time fulfil his function as the Priest. Imagine the situation. Aaron had watched Moses do it time and again, but now the responsibility was his. From now on Moses would no more engage in priestly duties, the onus would be on Aaron and his sons.
First he is to offer a purification for sin offering for himself, followed by a whole burnt offering. Cleansing from sin for himself must come first, and then atonement and reconciliation, dedication and tribute. But even as he offers these for himself he will be obtaining a level of atonement for the people, for it was to be ‘for yourself, and for the people'. As ‘the Priest' even in this he represents the people. Any offering for himself is therefore also on behalf of all.
But then he is to offer the people's oblation (their ‘required offering') finalising their atonement, finalising the covering before God of all their sin so that it is no more. It would be a process that would begin here and go on daily until sacrifices themselves ceased.