To create a new department:
Go to Contacts and click Directory to open the Directory structure
Click +Add Department in the top right corner of the main Directory dashboard. The Add Department to Directory window will appear

Type in the name of your new department
Use the toggles to set the rules for the department. If you wish to add contacts at this time, review steps 5-9. If you do not wish to add contacts, skip directly to 9
Switch on Include contacts toggle
Click +Add Contacts to Department. The new window with a list of contacts from your Directory will appear
Click ➕ next to the contacts you want to add to this department and click Continue

The number of contacts you are adding to the department will be displayed next to Contacts added line. Click View to double-check the list of these contacts
Click Create Department. The new department will appear in your Directory

See also how to Delete a Department or how to Add or Delete Contacts of an Existing Department.