After you have installed Tag Groups Premium, you can safely uninstall the free Tag Groups plugin. You may also keep it, but you have to leave it deactivated.

All the data from the free plugin will be carried over to the premium plugin.

Before you remove Tag Groups, please make sure that you have not changed the default settings that determine whether to erase the data during deinstallation. Go to the Tag Groups (Premium) settings and there to the "Reset" tab. All checkboxes should be deselected.