By default, notifications will only appear for new messages in the Focused Inbox. If you want to be notified of all new messages:
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Within our app, tap Settings.
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Under Mail, tap Notifications.
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Change Mail Notifications per account to All, Focused Inbox Only, or None.
You may also need to change your setting in the Android System for Notifications. This is different for each device, but please check that your system settings allow for Outlook to receive notifications.
To learn more about Focused Inbox, please see this link.