System satisfied Head of Department at first (6)
I believe the answer is:
method
'system' is the definition.
(thesaurus)
'satisfied head of department at first' is the wordplay.
'satisfied' becomes 'met' ('meet' can be a synonym of 'satisfy').
'at first' suggests taking the first letters.
The initial letters of 'head of department' is 'hod'.
'met'+'hod'='METHOD'
(Other definitions for method that I've seen before include "Fashion" , "rule" , "Process, esp. Stanislavsky's" , "Orderly procedure, sometimes found in madness" , "Way of doing something, technique" .)