Hi,
If you have already tried re-adding your account on the Outlook app for your mobile, please try to clear the cache and data of your Outlook app on your mobile, then restart. Try to log in again and observe for a few hours if it has already synced the emails.
If the issue persists, please check if there is an update for the Outlook app.
If it is already updated but remains the same, please try to reinstall the app.
- Uninstall the Outlook > restart your phone > install the app.
- Observe for a few hours to see if it has already synced the emails.
If you need more assistance, please let me know.
Stay Safe!