Just to clarify my thinking, did you purchase directly from McAfee? I have a active subscription which has a expiry date of 2018, which runs consecutively. It may be that in your case all you would have to do is just before your expiry date, of your currently installed subscription.
Remove the near to expire/expired subscription, and then install the next one.
You can also contact Customer Service/Technical Support free of charge https://service.mcafee.com/webcenter/portal/cp/home/contact
All the Best,