Capital this writer’s invested in Hollywood setting (4)
I believe the answer is:
lima
'capital' is the definition.
(capital of Peru)
'this writer's invested in hollywood setting' is the wordplay.
'this writer's' becomes 'im' ('I am' referring to the writer of the clue).
'invested in' indicates putting letters inside.
'hollywood setting' becomes 'LA' (Hollywood is a neighbourhood of Los Angeles).
'im' inserted inside 'la' is 'LIMA'.
(Other definitions for lima that I've seen before include "Mail to Peru'd capital" , "Peruvian capital" , "South American capital" , "Send mail out to S America" , "city (like 22)" .)