App Update does not Start
See App Stuck Installing / Update Freezing if update is stuck installing.
Please make sure you're using same Apple ID used when originally downloading!
It's an iTunes and not an app issue, below you'll find how to solve it.
Reboot your device
After checking the most common reasons for an app not to update or download completely, it is time to go with the most popular troubleshooting step: reboot the device. Remember, it is not enough to simply suspend the device and wake it up again. In order to give the device a full refresh, you will need to power off the device by holding down the sleep/wake button for several seconds and following the instructions on the screen. Once it is fully powered down, you can boot it back up by pressing the sleep/wake button again. This process will give your device a clean start and has a tendency to solve many problems.
Sign out of your Apple ID
If going through the authentication process by downloading an app doesn't work, sometimes simply logging out and logging back in will do the trick. You can sign out of your Apple ID by going into the device settings, choosing iTunes & App Stores and tapping where it displays your Apple ID. This will bring up a popup menu that will allow you to sign out. Once you are signed out, sign back into your Apple ID and try updating the app again.
Delete the app and download it again
Please make sure to backup your settings first, see Backup & Sync App Settings
Reset all settings
The next trick is to reset the device settings. Don't worry, this won't completely wipe your device, but because it clears settings, you will lose any settings previously customized. You will also need to sign back into websites that ordinarily remember your account settings. But other than clearing out your settings, this process will leave all of your apps, documents, music, movies and data alone.
To reset your settings, go into the device settings and choose General from the menu. Next, scroll all the way down and tap Reset. On this screen, choose Reset All Settings. This will prompt you before continuing with the reset.