Hello Loyuk,
Thanks for joining Apple Support Communities. I saw your post about Apple Music and I'll be glad to offer assistance.
Does this happen on a particular Wi-Fi network, or do you get the same error on all networks? How about if you switch from Wi-Fi to cellular data?
You mentioned this happens when you try to listen to new music; are you still able to play songs you previously added to your library, or that you downloaded?
Depending on the answers to the above, there are a few troubleshooting steps that might help you out.
If you haven't already, you might try to Restart your iPhone, iPad, or iPod touch and then test again.
Also, try tapping Settings > [your name] > iTunes & App Store. Are you signed in with your Apple ID here?
Another possibility is checking for iOS updates. Are you using iOS 12.1.3 under Settings > General > About? If not, check out How to back up your iPhone, iPad, and iPod touch and Update your iPhone, iPad, or iPod touch.
I hope this helps!
Take care.