Support a first-class head of department (3)
I believe the answer is:
aid
'support' is the definition.
(to aid is to help or support)
'a first-class head of department' is the wordplay.
'a first class' becomes 'ai' (A1 - top quality).
'head of' says to take the initial letters.
The initial letter of 'department' is 'd'.
'ai'+'d'='AID'
(Other definitions for aid that I've seen before include "encouragement" , "Help or succour" , "charity" , "Relief" , "technique that can produce pregnancy" .)