If you are on iOS 7 and higher:
Settings > Notifications > C.A.T.S.: Crash Arena Turbo Stars > Allow Notifications ON/OFF

If you declined to receive notifications in the first place, try to reinstall the game and agree to enable the notifications in the tutorial. Do not be afraid; you will not lose your progress if you follow these steps:  

1. Write down your Player ID (i.e. John#12345) somewhere, so our Support team can restore account manually if something goes wrong. 
2. Make sure you are logged into your Apple account, and iCloud synchronization is turned on in the Options before deleting the game. 
3. Delete and reinstall C.A.T.S. from the App Store. 
4. DO NOT agree to progress restoration pop-up. 
5. Complete the tutorial and agree to receive notifications. 
6. Navigate to Options and turn on iCloud synchronization. 
7. You will see a pop-up asking whether you want to restore your progress. This time, tap "Yes."