Will my iPhone pro 13 with a korean SIM card work in South Korea

It should. Just check to make sure your iPhone is unlocked. Some carriers lock their sim slots so it can only take their sim cards.

Here is Apple's insturctions on how to check if your iPhone is unlocked: "You can find out if your iPhone is locked by going to Settings > General > About. If "No SIM restrictions" appears next to Carrier Lock, your iPhone is unlocked."

Have a fun time in Korea. Also, I would highly recommend checking out esims if you are only looking for data.

It should work if it’s a Korean SIM card and your in Korea!