There is a simple step-by-step fix for Outlook not receiving emails in Office 365. Maybe the problem is your mailbox storage, so make some space. Open Outlook on your PC, and go to File. Click Info, then review the information under Mailbox Settings. Under the Properties menu, check the folder size. If the storage is full, delete some unnecessary messages. If using Outlook on web, click on Settings, then select General. Click on Storage, and if it shows 100% storage, find Deleted Items on the left sidebar. Select all and delete some messages.
For more info: https://helpemailtales.com/knowledgebase/outlook-not-receiving-emails-office-365