Big organisation involved in high tension chase (4)
I believe the answer is:
hunt
'chase' is the definition.
(I know that hunt is a more specific form of the action chase)
'big organisation involved in high tension' is the wordplay.
'big organisation' becomes 'UN' (United Nations).
'involved in' indicates putting letters inside.
'high tension' becomes 'ht'.
'un' placed inside 'ht' is 'HUNT'.
(Other definitions for hunt that I've seen before include "Organised search" , "Look high and low" , "Search; chase" , "track" , "Pursue quarry" .)