If YouTube videos are not playing on safari on your Mac, try these steps to fix the issue : 

1. Check internet connection : Ensure your internet connection is stable and working properly . 
2. Update Safari: Make sure you are using the latest version of safari . You can check for updates in the App Store.
3. Clear cache and cookies : GO to Safari>Preferences >Privacy , then click “Manage Website Data” and remove all YouTube playback . Try disabling them temporarily to see if that resolves the issue .
4. Disable Extensions : Some browser extensions may interfere with YouTube playback . Try disabling them temporarily to see if that resolves the issue .
5. Enable JavaScript : Ensure Java Script is enabled in Safari .Go to Safari >Preference >Security and make sure “Enable JavaScript ” is checked.
6. Update Adobe Flash Player: If you are using an older version of Safari , you may need to update Adobe Flash Player .However , note that Flash Player is being phased out and many websites, including YouTube ,have switched to HTML5 for video playback.
7. Restart safari : Close and reopen Safari to see if the issue persists .
8. Restart Your Mac : Sometimes a simple restart can resolve unexpected issues.
9. Try Another Browser : If the problem persists , try using a different browser like Google Chrome or Mozilla Firefox to see if the issue is specific to Safari .
10. Check for System Updates : Ensure your macOS is up to date by going to system Preference > Software Update . If none of these steps resolve the issue , there may be a deeper problem with your system or network connection , and you may need to seek further assistance from Apple Support or your internet service provider.