Doubt party accepts American president's first (7)
I believe the answer is:
suspect
'doubt' is the definition.
(I know that doubt is a more specific form of the action suspect)
'party accepts american president's first' is the wordplay.
'party' becomes 'sect' (I've seen this before).
'accepts' is an insertion indicator.
'american' becomes 'US' (United States).
'president's first' becomes 'p' (sst letter of 'president').
'us'+'p'='usp'
'sect' enclosing 'usp' is 'SUSPECT'.
(Other definitions for suspect that I've seen before include "Have qualms about" , "Doubt - man being questioned by police" , "Doubt - man held by police" , "One believed to have committed a crime" , "Imagine guilt" .)