Hover over Settings in the bottom left-side menu and click 'All Settings'

Select 'Board and Pieces'

Toggle off the 'Play Sound' option

Click 'Save' to apply the changes!

Tap 'More' in the bottom right and select 'Settings'

From the settings menu tap 'Board'

Toggle off the 'Sounds' option:

Go to your phone’s settings and tap 'Apps & Notifications'

Select the Chess.com app

From here, you can enable or disable notifications for the app:

Go into your Apple device's settings and tap 'Notifications'

Select the Chess.com app

From here, you can enable or disable move notifications, notification sounds, and badges: