It seems that the Free iOS App of the Week is gone in iOS 11. Apple started this back in 2012 as a way to paid apps that people may not otherwise buy. Apple showcased the app on the front page of the App Store. Once you downloaded it for free, it was in your purchased history. Even when the promotion ended you could still re-download it.
iOS 11 App Store
The App Store saw a big design overhaul in iOS 11. Games and apps are now in different categories, and there is a new Today tab. It shows behind-the-scenes app details, tips and tricks, and more. Instead of a free iOS app of the week, there is now an App of the Day, and a Game of the Day.
It’s possible that Apple could bring it back in a future version of iOS. Just like 3D Touch multitasking will come back, the Free iOS App of the Week could as well.