If the new update is not available to you after the game redirects you to the App Store, worry not. Just follow these instructions and you should be able to update: 

iOS 11 & 12:
- Go to your App Store
- Tap on the "Updates" on the bottom
- Tap on the screen and pull it down to refresh it
- Download the latest version of The Walking Dead: Our World

iOS 10 and older:
- Go to your App Store
- Tap on the "Updates" button 10 times to refresh it
- Download the latest version of The Walking Dead: Our World

If the update is still not showing for you, then it's because the update is on it's way to App Store in your region. Once Apple have pushed the update to your App Store then you will be able to download and install it. Sometimes this process can take a couple of hours.