Stigma inhibiting American support (7)
I believe the answer is:
sustain
'support' is the definition.
('sustain' can be a synonym of 'support')
'stigma inhibiting american' is the wordplay.
'stigma' becomes 'stain' ('stain' can be a synonym of 'stigma').
'inhibiting' means one lot of letters goes inside another.
'american' becomes 'us'.
'stain' placed around 'us' is 'SUSTAIN'.
(Other definitions for sustain that I've seen before include "Prolong, support" , "Strengthen; suffer" , "Keep alive" , "Strengthen, support" , "Maintain" .)