Miss Not-Appearing-in-the-Previous-Books finally appears in this one, and is a well-drawn character.
One thing that I found oddly endearing in both this book and the previous one is that every now and then, there'll be a mention of same-sex lovers. It's low-key, just "gay people exist in this setting, whatever" sort of thing. And it's nice to see a story where all the main characters are straight notice that not everyone in the world is.
Like the first book in the series, Republic alternates between a present-day story and one from the main characters' youth. For once, I didn't find the alternating of stories annoying. Both were engaging and I wanted to see what happened next in each, so there was no frustration from "get back to the INTERESTING stuff". I actually found the arc of the young-Gentleman-Bastards story better-constructed and more satisfying, in fact.
The present-day arc was less satisfying. Mostly it reminded me of PCs being railroaded by a GM: "you have to do this or the uber-powerful NPCs will smoosh you, and there's no other special motivation to go along." This extended to the main characters seldom seeming as clever as they're supposed to be. Possibly my standards for "clever" are unreasonably high. I know I don't write this sort of story in part because my own attempts at clever plans are never brilliant enough for me.
The stakes were generally lower in this book, which I appreciated; I find the constantly-increasing-stakes trend in many sf&f series to be rather tedious. I liked the romantic subplot running through both past and present story arcs, which ran con-trope in some interesting ways.
The setting, as is usual with Lynch's work, is well-drawn and described. I get a nice sense of place and the world from his work, with good imagery interspersed with the story so that it adds to the narrative and doesn't bog it down.
This may be my favorite of the three books, but has the curious effect of leaving me uncertain about whether or not I want to read the fourth. That's in large part because the aforementioned uberpowerful NPCs look like they'll be ever-more important to the future installments, and I really hate them. This is purely a personal preference: it's not that they're badly written, I just intensely dislike watching ordinary people grapple with and (almost always) lose to the whims of demi-gods.
Anyway, the fourth book isn't out yet, so I don't have to decide for a while.
I'll give this one an 8 overall -- it's something like "9 for the past story arc where they're putting on a play, and 7 for the current-day story arc."