I’m currently in Korea. As a green card holder, I’d like to apply for a Reentry Permit.

A Reentry Permit must always be filed while you’re physically in the U.S. And since fingerprinting typically happens about 4–6 weeks after filing, you would need to either re-enter the U.S. and file it there, or have already been there when you filed and left afterward. So representation from abroad isn’t possible in principle — by regulation, this must be done while physically present in the U.S., so we’d recommend traveling to Guam to handle it instead.