Our O365 inbox is stating that it is "full" and not sending 2-way email, Can we delete old messages?

Summary: We have a storage issue with our inbox and it is stating full and not allowing emails to relay back and forth between ORC and Outlook.

Content (please ensure you mask any confidential information): Are we able to delete OLD messages without affecting those that have already been sent between ORC and Outlook? Will this cause any downstream impacts?

Version (include the version you are using, if applicable): 25B