Red-faced American in a state! (7)
I believe the answer is:
florida
'state' is the definition.
(US state)
'red-faced american' is the wordplay.
'red-faced' becomes 'florid' (I've seen this in another clue).
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'florid'+'a'='FLORIDA'
'in a' acts as a link.
(Other definitions for florida that I've seen before include "American state, capital Tallahassee" , "SE US state" , "Miami's state" , "Southern US state" , "bordering Alabama and Georgia" .)