British former Prime Minister missing last engagement (6)
I believe the answer is:
battle
'engagement' is the definition.
(military engagement)
'british former prime minister missing last' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'former prime minister' becomes 'Attlee' (Clement Attlee, UK prime minister 1945 to 1951).
'missing last' means to remove the last letter.
'attlee' with its final letter removed is 'attle'.
'b'+'attle'='BATTLE'
(Other definitions for battle that I've seen before include "Lengthy struggle" , "Struggle tenaciously" , "A fight between large forces" , "Major engagement" , "Military engagement" .)