Hello quietcave,
Thank you for reaching out to Apple Support Communities, and we'll be happy to help in any way we can. We understand you're having issues with playing Apple Music after changing devices. Are you using the same Apple ID you used to purchase the music? Did you allow the device to use Apple Music?
This article goes over how to access music on all of your devices: Access your music library on all your devices - Apple Support
"Access your music library on all your devices
If you subscribe to Apple Music, you can make your entire music library available on all your devices when you’re signed in with the same Apple ID. You can access your library any time you’re connected to the internet, or even offline, if you’ve downloaded your music.
Your music library can keep the following available in the cloud:
- Up to 100,000 songs, not including songs (or music videos) purchased from the iTunes Store; files can be no larger than 200 MB
- Matched songs (songs available in the iTunes Store, whether or not you purchased them there) at iTunes Plus quality (256 kbps DRM-free AAC) and other songs at their original quality
- Music videos purchased in the iTunes Store
- Playlists that include songs and music videos
- Smart Playlist rules, which are applied on the computer or device they’re downloaded to
Note: Not all features are available in the Apple Music Voice Plan. Apple Music and Apple Music Voice aren’t available in all countries or regions. See the Apple Support article Availability of Apple Media Services.
You can also make your music library available across devices with iTunes Match.
- In the Music app
on your Mac, choose Music > Settings, click General, then select the Sync Library checkbox. - If you don’t see this option, sign in to Apple Music using your Apple ID. You must be an Apple Music subscriber to access your music on your other devices using Sync Library.
- To turn on your music library on another device, do any of the following:
- Another computer: In the Music app
on your Mac, sign in to the iTunes Store using the same Apple ID that you used on the first computer, then choose Music > Settings, click General, then select the Sync Library checkbox.
- An iPhone, iPad, or iPod touch: On your device’s Home Screen, tap Settings, tap Music, then turn on Sync Library.
We hope this helps.
Cheers!