In order to replace the Premier version of Norton 360 with the Standard one, you first have to uninstall the existing copy of Norton 360 Premier Edition. Then you can install the Standard version and use your subscription activation code. The two products are different and therefore you cannot use the activation code of one to activate another.
Note: If you want to keep your Norton 360 settings, use uninstall from within Norton 360 programs folder to remove the Premier Edition while keeping your settings for the next Norton 360 installation.