Did you sign up through Verizon? Verizon doesn't automatically do that for you. See the information in https://www.verizon.com/support/apple-music-faqs/ including but not limited to the following:
Can I get the Apple Music promotion if I already have an Apple Music subscription through Apple?
Yes. You can still get an Apple Music promotional subscription 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.