To restore your game progress from the iCloud or Android Cloud, you must first save it there. You can toggle the cloud synchronization on and off in Options.

Here is how to restore your game progress:

1. Make sure that you are logged in with the same Apple or Google account as before.
2. Install CATS from the App Store or Google Play.
3. The game will automatically ask whether you want to restore your progress upon loading. Tap "Restore".

If you do not see the progress restoration pop-up, complete the tutorial and see if the restoration pop-up appears upon completion.

I tried restoring my progress automatically, but I still can't restore it

In this case, you'll need to contact the Support Team.
Please, launch the game, go to Settings → Help & Support → Chat icon in the top right corner. If you don't see the icon, open any FAQ section and it'll appear.
To go directly to the robohelper, which will speed up the restoration process, start a new conversation and type the following (without writing anything else): Restore progress or  Restoreprogress