It's possible to prevent users from seeing and using specific ticket types. This restriction applies to all users though. It's unfortunately not possible currently to set up restrictions for specific users. User permissions are set up globally. To prevent all users from being able to see and use a specific ticket type you can go to Configuration\Ticket Content. In the Ticket types section, for the ticket type you want to hide, select a different type in the drop-down. Once this is configured, users will not be able to select the ticket type in question, and all tickets of that type will be shown to them as the selected type.
We have an item on our customer wish list in regards to adding the ability to designate permissions or restrictions to specific helpdesk users that override global settings. I will link your post to this feature request to add weight to it. At this moment in time we don't have an estimated release date for this feature though.
