Hi denafromgilbert,
Depending upon your Apple Watch model and storage capacity, you may need to download the playlist you like to listen to while running. This ensures your Apple Watch has the music stored locally and doesn't rely on keeping a connection to your iPhone or cellular data to play. These instructions will help in this regard:
Add music using your Apple Watch
If you’re an Apple Music subscriber, you can add music using your Apple Watch.
Note: Adding music isn’t available in the Apple Music Voice Plan. For more information, see the Apple Support article About Apple Music Voice.
1. Open the Music app 
on your Apple Watch.
2. Tap Listen Now or Search, then navigate to music you want to add.
3. Tap a playlist or album, tap 
, then tap Add to Library.
4. A message confirms that the item was added.
5. Note: You can stream music you add to Apple Watch when you have an internet connection. To play music when you’re not connected to the internet, you must first download it.
6. To download the music to Apple Watch, tap again, then tap Download.
Add music to Apple Watch - Apple Support
If you're still unable to play music, a few more details will help Apple Support Communities users like yourself assist.
- Are you able to play music from your Apple Watch with any other connected speakers or headphones? This will help us isolate between your Apple Music connection on your Apple Watch and the AirPods connection.
- Are you prompted to sign in with your Apple ID when you navigate to Watch app > My Watch > General > Apple ID on your iPhone?
Kindest Regards
