There are different ways how you can switch a license key from one active site to another.
Use the WP STAGING License Page
This is the most straight-forwarded way:
Go to the site dashboard where WP STAGING is active and open WP STAGING > License
Deactivate the license key:
Go to the site dashboard where you want to activate the WP STAGING license key and open WP STAGING > License.
Enter the license key and click on Activate License key:
Deactivate License key in Your Account
If you don’t have access to the active site any longer, you can activate it from your user account.
Login to your account and click on View Licenses
Click on Manage Sites
Deactivate the site you don’t want to use WP STAGING on:
After that you can activate the license key in your new website under WP STAGING > Licenses