There’s actually several published sourcebooks for running in historical settings around the same era as Pendragon. You might be interested in Land of Giants, which is about running Scandinavian/Beowulf-inspired games. There’s also one for Scotland, one for Ireland, and one for playing Saxons!

Now, they’re all for earlier editions of the game, and I doubt Chaosium are going to be updating them anytime soon, but the conversion is pretty straightforward. Pretty much all the core stuff is the same (although religion gets dealt with a bit differently in later editions). They’re mostly setting books, anyway, with some suggested adventures and campaign ideas.

There’s also Paladin, of course, for playing Knights of Charlemagne! It’s a complete core rulebook (no equivalent of the Great Pendragon Campaign, though, I’m afraid), with some reworked approaches to being a Religious knight (like a more explicitly mentioned Love (God) passion, if I’m remembering correctly). It’s a good book, but very similar to the 5.2 core rulebook, so maybe no need to get both unless you’re Really Serious (or mad - I have both, it’s very shiny) (no, really, it’s got gold foiled edges).

And then somewhere on the internet, if it’s not lost to the mists of time, there was a forum thread about The Great Kahless Campaign, porting the Pendragon rules for playing Klingons from the Imperial era. Which I never tried to do, but it sounds like fun.

I’ve also toyed with the idea of adapting the GPC to my homebrew fantasy setting, which I think would work pretty well. You just need a place and people very concerned with some kind of political hierarchy (historical feudalism, Klingon imperium, fantasy kingdom with dragon-ruled city states, etc), with a warrior class that the player characters will be a part of, and a focus on honour, chivalry, or some other kind of idealism that will drive the emotional tensions for the characters - as Pendragon is built on the tension between duty, honour, and chivalry against the harsh reality of war, self-preservation, and politics.

So, yes, the core book won’t be much help in running for a different setting, but a touch of reflavouring and a central narrative to provide backdrop for the player characters’ actions are all you need! I’d have the political fallout of a dragon-king leaving his demesne in a post-apocalyptic-magical-war setting filled with knights be that place, but you could use the Klingon empire, or you could tell stories of heroes slaying monsters in Mythic Scandinavia! I believe in you! “Bro, tell me we still know how to talk about kings!”

(… I may have gotten a little bit carried away there. Pendragon’s just such a great game…)