If you would like to use your Parallels Desktop for Mac license on a new Mac, you should sign out of the account the license is registered under on the Mac you don't need anymore.
Click on the Parallels Desktop menu, and select Account & License. In the activation window, click on your account email address and select Sign Out.
Now your license is available for use on a new Mac.
If you try to use the license on a new Mac without signing out of the old one, then upon activation on the new Mac you will see a warning that the license is already in use.
If you click on Activate on This Mac, the current copy will be successfully activated, and the license will automatically be deactivated on the old Mac.