To re-employ a past faculty member:

1.) Go to Core
2.) Users> Select  Edit User Profile Data 
3.) Search and select the appropriate user.
4.) Scroll to the lower left under System Information, and click the Employment link.
5.) Click the Employ button in the upper right corner.
5.) Enter Employment Information section will appear.
  • Enter the Effective Date/Time, or select Effective Immediately.
  • Enter the Date Appointed, and select all appropriate School Levels.
  • Under Employee Roles, check all that apply.
  • Under Departments, check all that apply (including Non-Academic Departments).
  • Under Grade Levels and Main Sports, check all that apply.
6.) Click Save & Exit in the upper right corner.

Also see: How to employ a new Faculty member? and How to add a New User or edit an existing user profile?