Hey gilgabuzz,
Thanks for using Apple Support Communities. I understand you're attempting to redeem an Apple Music through you wireless carrier. I'd be glad to offer some help. Once you redeem the subscription and link your Apple ID, you should be prompted within the Apple Music app to cancel one of your subscriptions. Cancelling with Apple will continue your Apple Music subscription with Verizon. It looks like the current subscription will end on Jan 25th and your new subscription through your carrier will begin. Your music and playlists will also carry over automatically as long as you sign-in with the same Apple ID.
I hope this helps.
Regards.