Fight a terrorist leader following search (6)
I believe the answer is:
combat
'fight' is the definition.
(combat is a kind of fight)
'a terrorist leader following search' is the wordplay.
'leader' indicates taking the first letters.
'following' means one lot of letters go next to another.
'search' becomes 'comb' (combing is a kind of searching).
The initial letter of 'terrorist' is 't'.
'a'+'t'='at'
'at' put after 'comb' is 'COMBAT'.
(Other definitions for combat that I've seen before include "Take action to deal with - fight" , "Conflict" , "Armed fighting" , "War; contest" , "Oppose" .)