Check your eligibility. In most cases the offer is only for new subscribers or those that have not previously used the free trial before. A free trial can only be used once, so buying another device will not give you another 3 months free. It is not available to current subscribers.
https://www.apple.com/promo/pdf/EN_US_ATV+_Promo_TandCs.pdf
I don't recall a time when the Apple TV+ service was not available without a free trial. You may be able to call Apple directly to confirm what free trial you used previously when the subscription was started. It may have been the case that you only used a week free trial previously, and may get the benefit of a prorated free trial to account for the 3 month offer.
Contact Apple Support - Apple Support
- New and qualified returning subscribers only. $9.99/month after free trial. Only one offer per Apple Account and only one offer per family if you’re part of a Family Sharing group, regardless of the number of devices you or your family purchase. This offer is not available if you or your Family have previously accepted an Apple TV+ 3 months free or 1 year free offer. Offer good for 3 months after eligible device activation. Plan automatically renews until cancelled. Restrictions and other terms apply.
Apple TV+ - Apple
