Arrogance of hot film director (7)
I believe the answer is:
hauteur
'arrogance' is the definition.
(thesaurus)
'hot film director' is the wordplay.
'hot' becomes 'h'.
'film director' becomes 'auteur' (I've seen this before).
'h'+'auteur'='HAUTEUR'
'of' acts as a link.
(Other definitions for hauteur that I've seen before include "Proud disdain" , "Surquedy" , "Lofty pride, looking down on others" , "Overbearing arrogance" , "Arrogance - Hutu era (anag)" .)