How to Redownload Apps After Restoring Your iPhoneby Jason Spidle
The iPhone restore functionality is a lifesaver if you ever suffer data loss or if you are upgrading to a new iPhone and it doesn't restore all your apps. If your most recent backup was made before the installation or purchase of software from the App Store, those apps are not included in the restore. Instead, you need to manually redownload the apps from the "Purchased" section of the App Store.
Tap the "App Store" icon on your iPhone home screen.
Select the "Updates" tab and then tap "Purchased."
Tap "Not on This iPhone" to view all purchased apps not currently installed on the phone.
Tap the cloud button beside an app to redownload and install the app on your iPhone. Enter your Apple ID password when prompted to do so. The app downloads in the background, leaving you free to continue reinstalling other previously purchased apps.