The following from Verizon may help: https://www.verizonwireless.com/support/apple-music-faqs/
(I don't know what happens if you cancel your plan first)
7 - Can I get Apple Music with my plan if I already have an Apple Music subscription?
You're still eligible to receive Apple Music with your plan even if you’re already a subscriber. Once you redeem the subscription and link your Apple ID, you'll be prompted within the Apple Music app to cancel one of your subscriptions. Cancelling with Apple will continue your Apple Music subscription on us.
and
8 - If I cancel my existing Apple Music subscription to enroll in this promotion with Verizon's offers, will I lose my saved music and playlists?
No, when you cancel your existing subscription your music and playlists will carry over automatically as long as you sign-in with the same Apple ID