To access Workflow and manage default statuses, you must have the ‘Manage system settings’ permission enabled in their role. How to enable permissions, see Roles and Permissions.

Adding statuses is part of workflow.

To add a status:

1. Go to User Menu | Settings | Workflow.
2. Click '+ New Status' beneath the list of available statuses:
3. Type a name for the new status.
4. Select a type for the status: Treat as Open, Treat as Completed, or Treat as Hold.
5. Select what items the status should apply to: Portfolio, Project, task, Issue, Request, or a combination of these.