Foreigner's broad smile on exit (6)
I believe the answer is:
gringo
'foreigner's' is the definition.
(gringo is a kind of foreigner)
'broad smile on exit' is the wordplay.
'broad smile' becomes 'grin' (I've seen this before).
'on' means one lot of letters go next to another.
'exit' becomes 'go' ('go' can be a synonym of 'exit').
'grin'+'go'='GRINGO'
(Other definitions for gringo that I've seen before include "Non-Spanish speaker" , "What the Mexican calls the American" , "English-speaker abroad" , "Latin-American term for English speaker" .)