had a free trial - do I get another with a new device purchase?

"Get 3 months of Apple TV+ for free." - Click on the link and read it, including the FAQ at the end. Check your eligibility. --> https://offers.appletvapp.apple/

"Only one offer per Apple ID 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 purchases. "

If you are asking about Apple TV+, no.

Free trials are not cumulative. Only one is granted per Apple ID.