Create a rule for each account you want to be notified on.

Turn off global notifications in Outlook's Preferences, Notifications and Sounds.To turn off all notifications and enable rules for specific accounts: Choose Do Not Notify from the list of actions. Choose Account from the list of Conditions then choose your account name.You'll need to create the Exchange account under Client rules to create this rule in Exchange accounts. Open the Rules dialog (from the Tools menu) and select the account you want to create the rule for.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.Click the System Preferences icon in your Dock or go to Apple menu > System Preferences from the menu bar. Choose Apply rule after messages arrive If you have an email account on your Mac you no longer use, you can delete or deactivate it.In the lower left of the Accounts dialog box, click. On the left-hand side of the window, select the account you want to delete. Next, create a rule for the accounts you want to receive a notification for. Delete an email account in Outlook for Mac. 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.

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