One who’s directing sexist perhaps to keep quiet (3,4)
I believe the answer is:
big shot
'one who's directing' is the definition.
(big shot can mean a boss or director)
'sexist perhaps to keep quiet' is the wordplay.
'sexist perhaps' becomes 'bigot' (sexist is a kind of bigot).
'to keep' means one lot of letters goes inside another.
'quiet' becomes 'sh' (both can be said to tell someone to be quiet).
'bigot' placed around 'sh' is 'BIG SHOT'.
(Other definitions for big shot that I've seen before include "Important man with loud gun?" , "Head honcho?" , "somebody" , "VIP, informally" , "Important person (with a large cannon?)" .)