Hello I have a license for avast internet security 7 for 3 pc still active, I can use it to avast 8 premier, I would not butttarla away and lose the remainder due.
The short answer is…yes. Sorry.
AIS and Premier are two different products and have different subscription rates.
You can always upgrade but you will need to pay full price. 
Give it a little time and there will most likely be a discounted upgrade path from AIS to Premier.