I've gotten this question a few times since I finished the core 'Gate' novels. As a fan who followed the series as it was being released, I can confirm that, in terms of the main narrative arc authored by Takumi Yanai, the core story is complete and doesn't have direct sequels or spin-offs written by the original author. The light novel series concluded, and that's the primary story of the JSDF's adventures in the Special Region.
However, the world of 'Gate' definitely expanded beyond just those books. The most significant spin-off is the manga adaptation, which isn't just a straight copy—it developed its own tone, leaned harder into certain political and military themes, and is sometimes seen as a companion piece with a different flavor. There's also the anime, which covers a portion of the story. But if you're hunting for more prose, the landscape is different. You'll find a lot of fan-created content and discussions online, exploring 'what-ifs' or continuing adventures, but nothing official from Yanai that continues beyond the final volume.
That said, the core series itself is quite long, so if you've only watched the anime, there's a wealth of material in the later light novel volumes that the show never reached, filled with larger-scale battles, deeper political intrigue in both worlds, and more resolution for characters like Rory and Tuka. So while there aren't official sequels, diving into the untouched parts of the original novels might feel like discovering new territory, especially the detailed fallout of the Ginza incident and the more complex treaties that follow the initial conflict.