Delete some of your emails and empty your "Deleted Items" folder to reduce your mailbox size. After deletion, you can check your mailbox size as described in the webpages below-
For Exchange 2013 users:
Alternately, you can register for using our email archive service which currently provides unlimited archive disk storage space. You can visit our webpage at https://www.its.hku.hk/documentation/guide/email/archive-2013 to understand more on how to use the email archive service. If you are interested in using this service, you can register for using email archive service by following the instructions below -
a. Login HKU Portal at https://hkuportal.hku.hk.
b. Type “archive” in the Search field
c. Click the link "Register for Email Archive".
For Exchange 2013 users who are already using the email archive service, please adjust your email archive policy to shorten the archive period so that more emails can be archived to release more disk space in your mailbox. You can refer to the steps at https://www.its.hku.hk/documentation/guide/email/archive-2013.