Support American backing up smear (7)
I believe the answer is:
sustain
'support' is the definition.
('sustain' can be a synonym of 'support')
'american backing up smear' is the wordplay.
'american' becomes 'us'.
'backing up' shows that the letters should be reversed in order.
'smear' becomes 'stain' ('stain' can be a synonym of 'smear'**).
'us' reversed gives 'su'.
'su'+'stain'='SUSTAIN'
(Other definitions for sustain that I've seen before include "Strengthen physically" , "Nurish" , "Withstand" , "Feed, nourish" , "Maintain" .)