For an admin to view and reply to support tickets in a specific department, you must assign it to them.
For more information, see Administrators and Permissions and Support Tickets.
Assign Support Departments
To assign support departments to an admin:
1. Go to Configuration > Manage Admins:

3. Edit the desired admin. A list of support departments will display.
4. For Assigned Departments, check one or more support departments.
6. Click Save Changes.