How do I reactivate Prism after upgrading to the new user based license model?
You just need to simply sign out and sign back in using your prism account email address.
Step 1: Go to Help -> Manage License

Step 2: Click the option to change activation
If you are on the legacy model, this screen would show a partial serial number and a machine ID.

Step 3: When prompted, sign in with your email address and password

Activation: Once you login with your Prism account email and password, you instantly get access to all the benefits of your new plan, including the ability to use Prism on up to two devices. Learn more about the new GraphPad Prism plans.