The Psalms have, not surprisingly, inspired many hymns and worship choruses. This page includes several playlists from Spotify that may help you to put these ancient texts into more modern melodies.

When you study a new psalm, take some time to conclude your study by listening to a few. Perhaps you'll find something that will help you to remember and sing the psalms to yourself as you go through your days. On the other hand, you may discover as I have, that some of our favorite choruses are out of context! Whatever the case, I hope that these will help you to appreciate the psalms as music.

From PrayPsalms:

Every Psalm From Poor Bishop Hooper:

This couple has written a song based on a psalm almost every week. In less than three years, they completed their project. You can read more about it on their website, Every Psalm.

From The Psalms Project:

This is a collaborative playlist of psalms from a variety of sources.