Apple Music

The Apple Music service is linked to your Apple ID account. Apple Music features will not be available to you when using a different Apple ID.

Additionally, using Apple Music and similar services creates a ‘long lasting’ link between the device and the Apple ID (“associated devices”). You are not supposed to switch Apple ID accounts regularly. You would be warned with a pop-up message when you try to. You may find yourself locked out of the service on that device if you try to associate the device with a different Apple ID within 90 days of the last association.

If you signed in but didn't associate the device (use associatable services) with the other Apple ID, then you can sign out, and sign in with the Apple ID that has the subscription. Then you would get the old subscription back.