To move a product license to a different computer, deactivate the serial number on the old computer, then use it to activate the product on the new computer.
If you are having problems activating a product on a new computer you can log in to your account on the Redgate website. There are two ways to help you, depending on the product and version you are using:
free up a license by removing a user who is no longer using the product
enable an extra activation for your serial number
You may need to contact your license administrator if you aren't the person who bought the product.