Enemy possibly of an egghead (3)
I believe the answer is:
foe
'enemy' is the definition.
(thesaurus)
'possibly of an egghead' is the wordplay.
'possibly' is an anagram indicator.
'an egghead' becomes 'e' (head letter of 'egg').
'of' is an anagram of 'fo'.
'fo'+'e'='FOE'
(Other definitions for foe that I've seen before include "Am archaic enemy" , "Opponent" , "Evil rival" , "opposing side" , "Antagonist" .)