Eccentric US president having tirade about Republican (8)
I believe the answer is:
aberrant
'eccentric' is the definition.
(thesaurus)
'us president having tirade about republican' is the wordplay.
'us president' becomes 'abe' (Abraham (Abe) Lincoln).
'having' means one lot of letters go next to another.
'tirade' becomes 'rant' (I've seen this before).
'about' means one lot of letters go next to another.
'republican' becomes 'r' (abbreviation).
'rant' after 'r' is 'rrant'.
'abe' put next to 'rrant' is 'ABERRANT'.
(Other definitions for aberrant that I've seen before include "Divergent from the normal" , "'Deviant, behaviour say (8)'" , "Wandering, straying" , "departing from standards" , "Deviating from what is accepted" .)