To create a rule for no notifications in a specific account In Outlook 2016 for Mac (and newer) you can create a rule to not display notifications or use the Outlook for Windows method of turning off global notifications and use rules for notifications. Repeat for the steps for each email account you want alerts on. Click Next again and complete the rule.Choose Display a Desktop Alert (and Play a sound, if desired) as the Action(s).Click Next twice to apply the rule to all messages sent to this account.Choose Apply rule after messages arrive.Next, create a rule for the accounts you want to receive a notification for. If you have Play a sound or Show an envelope in the taskbar enabled, you can turn those off too. In Outlook for Windows, turn off global notification in File, Options, Mail by unticking Display a Desktop Alert.