@KEZ7: Are you using the dedicated Outlook app? Also, if you sign in to your account via outlook.com (using a browser app), are you receiving emails as expected?
To troubleshoot the issue, please open your Quick Panel and make sure that 'Sync' is toggled on. Also, you may wish to try deleting some emails from your inbox, just in case the problem is storage related.
Have you tried going through Google 
