Will buying a new hardware stop my Apple TV+ subscription payment for a year? Apple is offering one year of free Apple TV+ with new hardware purchases at the moment. My question is, when I purchase a new qualified device, will Apple stop charging me for subscription fees for 12 months?
Will buying a new hardware stop my Apple TV+ subscription payment for a year?

No. If you are already on a paid subscription plan, you don't get a free year of Apple TV+.
The free year offer is only made available to new users, and is available only if you have not availed of a free trial or a paid subscription before.