In case you are paying the cellular plan for your partner on his iPhone, he can set up the watch with his Apple Account after you removed the watch from your Apple Account, if you already paired the watch to your iPhone.
The cellular plan for the Apple Watch has to be supported by the iPhone carrier.
Apple Watch - Carriers - Apple
What to do before you sell, give away, or trade in your Apple Watch, or buy one from someone else - Apple Support
If you did not set up and pair the watch to another iPhone at this time, and you used your Apple Account to buy the watch online from Apple, he can set up the Ultra with his Apple Account as well.
Set up your Apple Watch - Apple Support