I’ve not heard about the Apple Card offer, the free one year has been offered with the purchase of iPhone, iPad, Apple TV, Mac or iPod touch. if you say this was offered for activating a card then try the following steps:
Redeem your free year of Apple TV+ now.
Apple TV+ debuts on November 1. So your free one-year subscription can start on or after that. Here’s how to redeem it:
Turn on your new Apple device and sign in with your Apple ID.
Open the Apple TV app. Make sure your device is running the latest version of iOS, iPadOS, tvOS, or macOS.
The offer should be presented immediately after launching the app. If not, go to the Apple TV+ channel page where you’ll see the offer.
Tap Enjoy 1 Year Free.
https://support.apple.com/en-us/HT210573