Old designer leaving Italy to make scent for Americans (4)
I believe the answer is:
odor
'scent for americans' is the definition.
(US spelling of 'odour')
'old designer leaving italy' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'designer' becomes 'dior' (dior is a designer brand).
'leaving' suggests deleting specific letters.
'italy' becomes 'i'.
'dior' with 'i' removed is 'dor'.
'o'+'dor'='ODOR'
'to make' is the link.
(Other definitions for odor that I've seen before include "Stink in US" , "Pong in Ohio" .)