Fresh source of milk in part of America (3,6)
I believe the answer is:
new jersey
'part of america' is the definition.
(US state)
'fresh source of milk' is the wordplay.
'fresh' becomes 'new' (synonyms).
'source of milk' becomes 'Jersey' (Jersey cow).
'new'+'jersey'='NEW JERSEY'
'in' is the link.
(Other definitions for new jersey that I've seen before include "Recently-purchased clothing" , "The Garden State" , "change of clothing" , "Newark's state" , "calf?" .)