See: Bundle Apple subscriptions with Apple One
If you already subscribe to Apple Music, Apple News+, Apple Arcade, or Apple TV+, you don't need to cancel those subscriptions. They will automatically be canceled when you're billed for Apple One.
Commencing with Apple One migrates you from your existing service subscription (which is terminated at that point) to your new Apple One subscription. Remaining time on the exiting subscription will be refunded. This is mentioned with regard to iCloud + as an example in What happens to your iCloud storage when you sign up for Apple One: Your current iCloud+ plan will be cancelled and you'll receive a pro rata refund.