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 worry, you will not lose your progress if you follow these steps:  

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