Capital this person’s invested in American city (4)
I believe the answer is:
lima
'capital' is the definition.
(capital of Peru)
'this person's invested in american city' is the wordplay.
'this person's' becomes 'im' (('I am' - 'this person' means the crossword setter).
'invested in' is an insertion indicator.
'american city' becomes 'LA' (short for Los Angeles).
'im' going within 'la' is 'LIMA'.
(Other definitions for lima that I've seen before include "Mail to Peru's capital" , "Mail it to Peruvian city" , "Kind of bean" , "city (like 22)" , "Send mail out to S America" .)