The support contract is unrelated to the ability to install on additional machines. Most licenses entitle you to activate a Matlab installation on several machines (the precise number depends on the type of license you have).
If you've only installed on one machine, you should be able to download and install on a different machine without any kind of update in license status. Moreover, if the other computer has been retired, you can also go online and deactivate it from your Mathworks account (assuming you have admin privileges over the license).
