Carrot and Angua get married, but Carrot confesses to Angua he's having second thoughts due to the job. Angua tells him he just has to accept their both officers of the law. He denies that's the problem and she probes deeper. It turns out he's a bisexual and romantically attracted to Commander Vimes and wishes that Vimes didn't have a wife; surprisingly Angua agrees, she'd have gone for Commander Vimes if Carrot wasn't there for her. The two of them grow even closer over this revelation. <3

Carrot doesn't take the throne, his son ascends to Patrician thanks to Vetrinaris meddling. Before the Big Black V bought the bucket of barnyards he set out some specific requirements for the net head of the city that lead to Captain Carrots son being the front runner (being a watch commanders son counts as military eperience, nobility to the Ironfoundersons, etc). Vetrinari dies after abdicating to a transitionary legislature of dual house of council of wizards and popularly elected officials in the lower house and guild-representatives with nobles in the upper house (because Wizards keep the populism in check, while commoners distrust magicians with too much power, but putting them in the same house gives them a common cuase against the nobles/guilds [who can suffer populism or manipulate it]).

Or whatever, Vetrinari could manipulate Bloody Stupid Janette (BSJ's grandaughter) to make a computer regent until the king is revealed and I would still be happy if Carrot got to be happy as he knows how (policing) but returned him to the throne.

But the monarchy maybe a constituional monarchy instead of absolute monarchy, because I think that's what Prattchet was at least going to transition through (if not on his way to a full republic).

Eventually Ankh Morpork becomes the equivalent of New York with the UN, but instead of being the mediator in conflicts they are the Arbitrator giving the world decisive geopolitical actions they once reserved to believe in the gods for.

The Gods of the Discworld look upon this and smile, because humans think we are in control of our lives. Their games will continue, but now there is a bigger gameboard instead of a few smaller ones. Eventually this Pax Morporkia age will die, but until then the are glad to have the full disc as a board, instead of transferring paused games from continent to continent and having to take out and blow on a cliff before reinserting it to get it to work.

Lay Sybils Dragons are slowly regaining their nobilis traits but it will take quite a long time to make them into Draconis Nobilis or anything like that rather than poor swamp dragons. These secrets will be carefully guarded to gain dragon breeders of Ankh Morpork and the Vimes house money and prestige, but they do see a lot of the money continue to fund the abandoned dragons house (they're not tossed aside for business).

The Thieves guild is made obsolete by the bank that Moist von Lipwig set up. The Assassins guild id eventually militarized by the government for a minor brushwar but returned to its status when it's revealed that they're not going to be a viable military force since they work best in friendly urban settings (but will gladly take government jobs). The Clowns Guild reintroduces mimes on the shortest leash after Vetrinari, with King Carrots reforms allowing them some leeway (but not a lot). The guild of alchemists is given a partnership with Unseen University to get themselves some blastproof buildings, with a building dedicated to Leonard of Quirm.

Nobby and Colon continue to be essential a bit after their retire, Nobby having cured some medical conditions but getting others (namely, children) and Colon lives to see his son become Captain of the Palace guard (for Carrots son as King) proud as a polished hippo on the bridges.

Moist von Lipwig becomes city Treasurer for a bit, but leaves, only for his son to be a Drummknott-level advisor to King Carrot. Mister de Worde finds himself approached by the librarian who wants to try an experiment involving magically-enhanced clacks to spread a newspaper, and gives his son an insiders look (for an advantage in the biz) into this new Disc-wide reporting service.

And and and...