Within Teamwork Desk you can add new custom ticket statuses, in addition to the default ones.
To create a new ticket type, click on your profile image to the far right of the Desk navigation bar and select 'Settings':
Select 'Company' from the setting options:
From the left pane select 'Ticket Statuses':
You will now see a list of current Statuses such as:
To add to these, type your new ticket status name into the bar at the bottom of the current list and then select the green 'Add' option to the right of the bar:
Once you have selected add, the new status will appear on the dropdown list in a ticket.
When viewing a ticket, you can now change the status to the newly created one:
For more information see: Creating new ticket statuses