Director’s shoot perhaps screening four (9)

I believe the answer is:
executive
'director's' is the definition.
(thesaurus)
'shoot perhaps screening four' is the wordplay.
'shoot perhaps' becomes 'execute' (I've seen this before. I am not sure about the 'perhaps' bit.).
'screening' indicates putting letters inside (inserted letters are covered or screened by others).
'four' becomes 'IV' (Roman numerals for four).
'execute' enclosing 'iv' is 'EXECUTIVE'.
Can you help me to learn more?
(Other definitions for executive that I've seen before include "Having the power to put plans or actions into effect" , "Big guns" , "administration" , "boss" , "Senior manager" .)
