Leader heard Republican missed out (4)
I believe the answer is:
head
'leader' is the definition.
(I know that head is a type of director)
'heard republican missed out' is the wordplay.
'republican' becomes 'r' (abbreviation).
'missed out' suggests deleting specific letters.
'heard' with 'r' removed is 'HEAD'.
(Other definitions for head that I've seen before include "Lead - school principal" , "Edible part of cabbage" , "See 14" , "Source of river, leader" , "Chief; part of body" .)