In this chapter, Aaron and his sons are consecrated as priests.
When I first read this, I thought it was a duplicate with the content of Ex 40, but I double-checked and it turns out that in Ex 40, the LORD commands Moses to anoint the priests and the tabernacle and all of the various things that go in the tabernacle, but he doesn't actually do it there. Of course, temporally I think this chapter is a continuation of Ex 40, so the gap in time is probably very small (while the gap in chapters is large). Ex 40 concludes with Moses constructing the tabernacle and it says that "whenever the priests entered the tent of meeting... they washed", but this is a general statement related to process, and not regarding any particular event or time when "they entered". Instead, the consecration is presented to us here, which is discontinuous from Exodus, yet I think it does fit into context here because Leviticus is the book of the priesthood. While I think it would have been more complete to include this account in Exodus, I don't think it's out of place here either for that reason.
That said, this chapter is substantially identical to Ex 29, just as Ex 36-39 were substantially identical to Ex 25-28 and 30. Everything that is described in this chapter, all of the details of the four offerings (bull, two rams, grain), the anointing process and the seven days of ordination were described in Ex 29 as well. The details of the sin offering, burnt offering and grain offering are also virtually identical to the same sacrifices in Leviticus. The one oddity is that the "ram of ordination" is not a sacrifice detailed in Lev 1-5, probably because it was extremely rare (only had to offer it once per high priest). Even so, I noticed that this offering was largely similar to the peace offering of Lev 3, with the fat all burned and the meat eaten by the offerers (in this case, the priests). The big difference is how the high priest and his sons are painted with blood in this peculiar way, but other than that it pretty much is a peace offering. With that, we see that four of out the five core Levitical offerings are used to ordinate the priests, only leaving out the guilt offering.
Already we can see that the sin offering is being used in a much broader sense than it was stipulated in Lev 4, because in Lev 4 we are told that it is for unintentional sin or violations of the Law. In this case, it is being used as an offering of atonement for sin in general. There is no particular sin they are atoning, it is just a, "we are a sinful people" kind of statement. The burnt offering and grain offering were already general when stated in Lev 1-2, so there's no difference here, and the peace offering is similar to the sense of Lev 3. The guilt offering is not made presumably because it is not applicable (no ceremonial uncleanliness).
This chapter is also an early example of the commingling of offerings that I described before. I talked about pairs of burnt and grain offerings, but we can see that the Hebrews had no problem merging together nearly all of the sacrifices at once. I previously talked about the various offerings forming a story, and we can partially see that here. The sin offering is made first, because they must atone for their sins before approaching the LORD. Then there is a burnt offering and grain offering, which I guess is sort of the core ritual offering, or maybe the binding of a contract (between the priests and God). Then they conclude with the "ordination offering", which is basically a peace offering, and that is the meal with God. As we saw in Gen 31 and Ex 24, eating a meal with someone is how you formally conclude a covenant (the contract between Jacob and Laban for one, the covenant between the people of Israel and God in the other). Eating the peace offering is therefore an apt conclusion to the covenantal assignment of the priesthood to Aaron and his sons.
This story is why the offerings (usually) must be paired together, because you cannot have a conclusion (peace offering) with an introduction (sin offering), and there is usually something in the middle too (burnt/grain offering).
For more thoughts on the topics of this chapter, please see my discussion of Ex 29, which I shall not repeat here.