To restore your game progress from the iCloud, first you need to save it there. You can turn iCloud synchronization on and off in the Options.

Here is how to restore your game progress:

1. Make sure that you are signed in under the same Apple account as before.
2. Install King of Thieves from the App Store.
3. The game will automatically ask whether you want to restore your progress upon loading. Tap "Yes".

If you are not seeing the progress restoration pop-up, complete the tutorial and make sure that iCloud synchronization is turned on in the Options.