Just bought and IPhone 11 Pro from Apple, how do I sign up for the free apple TV offer. Apple TV not allowing me to sign in.

Here’s a guide: Apple TV+ - One Year Offer - Apple

You first redeem the offer on your new device, in the Apple TV app.

If you qualify, and if you did as described in the guide, and you still do not get to see the year offer, then contact Apple Support. They can assist in getting you the service, if needed using activation codes.

Accepting the 7 day trial would forfeit the year offer, so I would advise to not do the regular trial of you qualify for the year.

Just starting watching without getting the subscription, may offer a few free access teaser episodes, but the full Apple TV+ catalog requires the subscription. You would receive a confirmation email after starting the subscription.