These links might be useful to you:
How to disable new email notifications for a specific account in Outlook?
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For disabling new email notifications for a specific account, you need to disable the new mail desktop alert for all accounts, and then create new mail desktop alert rule for all accounts except the specific one. . . .
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Disable New Mail Notifications for Some Accounts
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. . . . You can't disable notification for one account only (well, at least not in Outlook for Windows), but you can disable notifications for all accounts then create rules to display notifications for the specific accounts you want notifications for. . . .
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