Diet of family in South American city (6)
I believe the answer is:
skinny
'diet' is the definition.
(both can mean low-fat in the names of foods)
'family in south american city' is the wordplay.
'family' becomes 'kin' (synonyms).
'in' indicates putting letters inside.
'south' becomes 's' (synonyms).
'american city' becomes 'ny' (I've seen this in other clues).
's'+'ny'='sny'
'kin' put within 'sny' is 'SKINNY'.
'of' acts as a link.
(Other definitions for skinny that I've seen before include "far from stout!" , "Low-calorie white coffee -- sent any kilt (anag)" , "'Scrawny, weedy (6)'" , "stout? Certainly not!" , "Underfed" .)