You can achieve this through the following methods.
Login to the Care Diary login page and go to Staff > Profiles using the left menu. All the Staff profiles are displayed in the List tab. Click on the edit action for a Staff Profile you wish to archive.
Once you open a staff profile, you must navigate to the Archive/Unarchive tab.
Finally, you can hit the Archive button and this staff profile will be moved to Archived Staff Profiles.