Using the New Outlook for Mac features in business environments
Dear Kate8634
Welcome to Microsoft Community.
Based on your feedback, you are currently experiencing an issue with Outlook showing a storage space warning.
Regarding your issue, in addition to the 15 GB of free Outlook.com email storage, Microsoft also provides an additional 5 GB of cloud storage.
If the 5 GB of cloud storage is full, even if the 15 GB of Outlook storage is sufficient, you will still receive a message indicating that the cloud storage quota has been exceeded and you will be unable to use it.
You can choose to release space in OneDrive by going to the Outlook web version, clicking on Settings > General > Storage. Additionally, check if OneDrive is being used on your computer by looking at the bottom right corner. If OneDrive is in use, please disable it and then release space through the Outlook web version.
If you have already released space and still cannot use Outlook, you may need to wait for a while. It is recommended to wait 24 hours before trying again.
You can refer to the link:Storage limits in Outlook.com - Microsoft Support
Feel free to text back if you need further help.
Best wishes
Chris.S-MSFT | Microsoft Community Support Specialist