Something I've learnt over the last year is that nobody's really managed to replace Risk in the way I want. Game of Thrones is definitely the best I've played (especially the combat system) but there's still work to be done in that space. I need to try Rex at some point because it looks like it captures some of the same things Game of Thrones does, but at the same time you're less mobile and it seems like your positions are a lot more fluid. The game I always have an eye out for captures the same feeling of accruing and losing territory that Risk does.
Nexus Ops is definitely worth looking into. It's a dice roller like Risk but with different unit types, varied terrain, and secret objectives for scoring. The small map makes for a quick (60 min) game.
Another option is Antike (II), which has more of a territory control (as opposed to purely conquest) element, but features more Civilization-esque gameplay (tech trees and a simple economy). No dice or other random factors, though, and still short (90 min).
Small World is Risk-like, but largely without dice. Instead the draw are the various factions with interesting combinations of abilities. You'll get to bring in new factions at particular points in the game as well.
None of the above offer alliances or betrayal aspects, though. Eclipse does, but it's a longer (3 hour) game with a 4X focus. There's also Cosmic Encounter, but that loses the board entirely and goes all in on zany powers and table diplomacy.