The title captures the issue.
I see this question: How can I repeat a Playlist?
and this question: Repeat on iOS 8.4 music app?
both from a legacy version of iOS (8.4). It appears that the music app interface has changed in newer versions of iOS (I'm currently running 10.1.1).
Best Answer
Open the Music app, then go to Library -> Playlists -> [Choose your playlist]. Click on the first song to start playing the playlist. At the bottom of the screen, the song currently playing will appear. Click on it. This will bring up your classic playback information (album info, tracking slider, volume slider). Then scroll down by sliding your finger up the screen. Right underneath the airplay symbol are two buttons: Shuffle and repeat. Click the repeat button.