Movie director's challenge, after initial and final cuts (5)
I believe the answer is:
allen
'movie director's' is the definition.
(Woody Allen the American film director)
'challenge after initial and final cuts' is the wordplay.
'after initial and final cuts' says to take the centre (cut beginning and end and get middle).
The middle of 'challenge' is 'ALLEN'.
(Other definitions for allen that I've seen before include "Woody ... is film director and comic actor" , "Woody ..., US film maker" .)