1. Login to Zimbra admin panel, then click on Manage.
1. Now click on the dropdown list on the left hand side corner of the window and choose New.
1. Choose your Account name and your domain name if you have multiple domain.
2. Put first name in the First name field.
3. Put last name in the Last name field.
1. Put the password as per your choice then click on Next to reach to Advance tab.
1. Double click on the email address whose Mailbox size needs to be increased, now move to the Advance tab and put the desired value in the text field of Account quota(MB) then click on Finish.
In this way you can increase the account quota for a specific user.