Heads of education department guarantee exam advantage (4)
I believe the answer is:
edge
'advantage' is the definition.
(edge is a kind of advantage)
'heads of education department guarantee exam' is the wordplay.
'heads of' says to take the initial letters.
The initial letters of 'education department guarantee exam' is 'EDGE'.
(Other definitions for edge that I've seen before include "Margin, extremity" , "Move carefully; limit" , "The part farthest from the middle" , "incisiveness" , "Line where soething begins or ends" .)