Straying US president against Republican bluster (8)
I believe the answer is:
aberrant
'straying' is the definition.
(I've seen this before)
'us president against republican bluster' is the wordplay.
'us president' becomes 'abe' (Abraham (Abe) Lincoln).
'against' says to put letters next to each other.
'republican' becomes 'r' (abbreviation).
'bluster' becomes 'rant'.
'abe'+'r'+'rant'='ABERRANT'
(Other definitions for aberrant that I've seen before include "Departing from accepted standard" , "Departing from type" , "Irregular" , "Departing from the norm" , "Diverging from the norm" .)