This is a Prestashop Module customization work, we've already bought the commercial module "LofDeal", it comes with 3 different deal type: current, upcoming and past. Here is the module link [url removed, login to view], so you can get some idea.
What we need is to add a new deal type: "Featured Deals", the result will be:
1. Featured Deals -- This is actually part of the current deals, but will only show the latest week deals.
2. Current Deals -- This is rest part of the current deals except the latest week deals.
3. Past Deals -- Finished deals (this will keep the same as is).
4. Upcoming Deals -- (this will keep the same as is).