I use a free app for Android called “Podcast Republic” to listen to podcasts in Korean (and Japanese and English).
Download on Google Play: https://play.google.com/store/apps/details?id=com.itunestoppodcastplayer.app
From the side bar, you can change the country to Korea. And select “Top charts” to browse popular podcasts. Change genre from “All” to “Music” or whatever you like and subscribe to the ones that you like. You can also search for the name of the podcast (see the magnifier, on the top, beside “Top charts”?). I searched for “슈퍼주니어” because I couldn’t find “슈퍼주니어의 Kiss The Radio” among popular podcasts. I also like that I can stream the entire podcast from beginning to end or save it so I can listen to it offline. ###