See the following instructions from Verizon https://www.verizon.com/support/apple-music-faqs/
9-Can I get Apple Music with my plan if I already have an Apple Music subscription through Apple?
Yes. You can still get Apple Music with your Verizon plan even if you’re already subscribed through Apple.
Once you redeem the Verizon promotional subscription and link your Apple ID, you'll be prompted within the Apple Music app to cancel one of your subscriptions. Canceling with Apple will continue your Apple Music subscription through Verizon.
10-If I cancel my existing Apple Music subscription to enroll in this promotion, will I lose my saved music and playlists?
No, when you cancel your existing subscription your music and playlists carry over automatically as long as you sign in with the same Apple ID