I just purchased a new iPad which came with a free subscription to Apple TV. How do I cancel my current subscription which I’m paying for? Thanks for any help.

If you cancel a paid subscription you have access until the date you are paid (i.e., until the end of the current billing period).

If you cancel a free Apple TV trial then you lose access for the remainder of the trial period.

The free 12 Apple TV+ offer cannot be combined with other Apple TV+ free trial, but you don’t have to be a new customer - I canceled membership to use the 12 months free offer without any problem.

Here are Terms and Conditions:

https://www.apple.com/promo/pdf/EN_US_ATV+_Promo_TandCs.pdf

The one-year AppleTV+ is a one-time offer applied to your AppleID account. 

Whilst the offer is linked to the purchase of a qualifying device, ultimate eligibility is determined by your AppleID. If you have never previously had an AppleTV+ subscription, purchase of a qualifying device provides an opportunity to try the AppleTV+ subscription service, free, for a year; the offer must be redeemed within 60-days of initial activation of the qualifying device.

If you have at any time previously had an AppleTV+ subscription, under terms of the offer (see the small-print), you’ll not be eligible for this offer. Cancelling your current AppleTV+ subscription will not reset your eligibility - but will immediately cancel a paid subscription and lose access to content for the remainder of the period for which advance payment has already been made.

I hope this clarification is helpful to you.

Not sure if and how you can do it.

I suggest that you contact Apple directly and explain your doubts, using this link:--> Get Support

Regards

Giulio

Have you tried going to App Store - Subscriptions?

You should be able to see there what is active, and cancel what you don't want