The three month 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.
You can check eligibility here:
https://offers.appletvapp.apple/