If you wish that your clients should be able to submit tickets directly to a specific department without having the option to choose any department, the following direct URL can be used for ticket submission under one specific department:
http://yourdomain.com/index.php?/Tickets/Submit/RenderForm/<departmentID>
You can check the <departmentID> by hovering over the department name which will reflect the details at the bottom left corner of the screen.
Sukhpreet Anand