On reinstallation of Norton an addition instance of the same PC is added to the subscription.

If you are referring to the Devices page in your Norton Account, if you delete the wrong device, Norton will stop working on it. The good news is that you can delete both devices. Then from your computer open the classic 360 interface by right clicking the Norton icon in the system tray, then click on Settings > Subscription Status at the bottom right to reactivate your subscription on that device.