Hi Anna, this is Jeff. I also live in Korea and share an interest in permaculture~
To the best of my knowledge, and I've spent a bit of time searching and asking around, unfortunately, there isn't any permaculture community (in the sense that permies-types would consider) in Korea. There is a place that calls itself the Permaculture College. The founder did study permaculture in Australia and has written articles and texts about permaculture in Korean. I visited there once, and though I recognize the important work that they are doing, it wasn't anything close to the kind of hands-on project-based community that I was expecting.
There are a number of eco-villages in South Korea, as well, though many of them are organized around a religious core more than anything else.
As far as functioning communities, the Mindeullae 민들레마을 was among the most impressive. It is an intentional village that runs an alternative high school, grow their own rice and wheat, run a collective bakery who's products help fund the community. And they are the home to the ATC, Alternative Technology Center. They even have a week where the students are banned from using electricity and have to make due with alternative technology systems only.
Alternative Technology Center Korea
It seems that there is a growing interest in permaculture in Korea. Independent study groups have been spring up. More than once, permaculture instructors have been flown out from Australia to give PDC courses. There isn't however, a consistently conducted course. Part of the problem is a lack of material in Korean, and part of the problem is that permaculture hasn't been made to seem relevant to the Korean context.
Nonetheless, Korea has a vibrant natural farming movement. There has been a back to the land movement happening for a while.
There is a fermentation-based farming method known as Korean Natural Farming that has gained quite a bit of popularity abroad.
Korean Natural Farming
All of the elements of permaculture that we know and love are out there, earth-building, no-till farming, food foresting, just not collected together in a comprehensive way.
If you know Korean, I could refer you the few articles and resources that I'm aware of. I'm not Korean, but I can speak it decently. I'm sure there amazing stuff happening that I'm just not aware of yet. I'd love to find more people who wanted to help grow a Korean-relevant permaculture.