Use internal storage for mail

Is this an Outlook Exchange account? If not what type of email account is this? Is the account configured as POP or IMAP? Are you saying you have reached the limit of what the server will save for your account?

Depending on how your account is set up you can either 1) just delete the mail on the server and Outlook will keep it locally in the .pst file for the account, or 2) you can export the account to an offline .pst file that you can open in Outlook and treat as a backup file, then delete mail on the server account.

But it depends on how you're configured.