This chapter begins by giving us a list of Solomon's officials, which is conceptually similar to the two lists of officials under David that we read in the book of Samuel. Some of these names are familiar, and some are not. First of all, "the priests" are listed twice. First we are told "the priest" is Azariah son of Zadok, and second we are told that "the priests" are Zadok and Abiathar. This is weird. In 1 Kings 2 we were told that Abiathar was removed from the priesthood, which suggests that the list of officials is probably taken over a time range in Solomon's rule, and not at a single instant. It's also not strictly chronological, because Abiathar has already been removed. Therefore this list is probably the set of officials that served under Solomon for some time period, both previously and into the future. More likely than not, Abiathar was removed from the priesthood and some time later, Azariah succeeded his father as the high priest.
Secondly, Benaiah remains over the army since Solomon assigned him in 1 Kings 2.
None of the other names are very familiar to me, and they are only given passing mention in the bible. Instead of focusing on the people in Solomon's court, I think it's more instructive to look at what kinds of officials are important enough to mention. Most of the roles are similar to what existed under David, but a few are new. The "deputies" are a new administrative role created by Solomon. This shows an increasing structure and probably also increasing scope of authority that exists under Solomon compared to David. Perhaps even more tellingly, Solomon creates a minister over "forced labor", which sounds vaguely ominous to me. This implies to us how Solomon managed his vast building projects on the one hand, and his somewhat authoritarian rule on the other hand. As we will later see, Solomon primarily conscripts his own people into forced labor, though it's possible that he also enslaved other peoples. I’d also like to point out that “the king’s friend” is an official role, and we can reflect on this that the various “friends” of king David were probably also officials in his court, even though they weren't mentioned in David’s lists of officials.
The twelve deputies are entirely unknown to us, as far as I can recall, and I don't believe they are mentioned anywhere else besides their role as Solomon's officials.
The rest of this chapter is primarily devoted to telling us about how great Solomon was. Apparently he ruled over a very large area, had tremendous wealth, and was renowned across the world for his great wisdom and poetic creation, as well as various botanical and biological manuscripts. I don't think I have much to say about this except for one point, which is the horses.
Gathering a large number of horses certainly fits the theme of this chapter, which is emphasizing Solomon's wealth and power. However, what makes this part a bit different is that it appears to contradict the LORD's command in Deuteronomy 17:16. David, for his part, captured many horses but then hamstrung all but a few hundred.
This passage, however minor and incidental it might seem, should concern us. Solomon does not appear to be following the Law completely, and his behavior may arouse the anger of the LORD at some later time, even though he is not being rebuked for it right now.
Even so, it appears that everything is going great for Solomon so far. His vaunted wisdom is paying off not just with his intellectual accomplishments and fame, but also with very real military and economic power. This is almost definitely the apex of Israel's historical power and it certainly shows in these descriptions, and nearly the rest of his life is going to be just as triumphal. It's only at the end of Solomon's story that we learn how his spiritual indiscretion is going to result in problems for Israel as a nation.