Much of Necessity is about exactly that - necessity, in the sense that the gods are bound by necessity to certain courses of action. There's a lot more about the nature of the gods, the flow of time, and the universe at large in this book than either of the others. Apollo, Athene, and an alien god are central figures in this book, taking a direct hand in much of the story.
The viewpoint characters in Necessity are almost entirely new. Other than Apollo, none of them were the narrators in the prior books. I particularly liked that Walton used Crocus, one of the sentient machine Workers, as a viewpoint character in several chapters of this book. It was also nice to see the viewpoint of Jason, who is a "silver" citizen (practical work rather than the philosophy and leadership of the "gold" citizens) on Plato. The majority of the prior two books were written from the perspective of "gold" citizens, so that perspective was a bit different.
Unlike the first two books, Necessity doesn't end with a major shakeup affecting the Platonic cities. Appropriate for the final book in the series, but I'll admit that it felt a bit anti-climatic. After the way The Just City and The Philosopher Kings ended, I kept expecting some kind of bombshell in the last few chapters of this book. We do see the that aforementioned re-contact with other humans, which is certainly important, but it's not in the same class as the splitting of the city or relocation to a new planet.
The Thessaly trilogy won't be for everyone, but for those who enjoyed the first book, finishing out the series is well worth the read.
