Indifferent about a city in America American backed (6)
I believe the answer is:
casual
'indifferent' is the definition.
(thesaurus)
'about a city in america american backed' is the wordplay.
'about' becomes 'c' (abbreviation for 'circa'**).
'a city' becomes 'la' (Los Angeles).
'in america' becomes 'us' ('US' is part of 'america').
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'backed' shows that the letters should be reversed in order.
'la'+'us'+'a'='lausa'
'lausa' in reverse letter order is 'asual'.
'c'+'asual'='CASUAL'
(Other definitions for casual that I've seen before include "Informal, dress say" , "Informal as dress may be" , "Informal or cursory" , "Cursory or nonchalant" , "Informal like clothes" .)