Republican limit under president is an anomaly (10)
I believe the answer is:
aberration
'an anomaly' is the definition.
(I've seen this before)
'republican limit under president' is the wordplay.
'republican' becomes 'r' (abbreviation).
'limit' becomes 'ration' (rationing is a kind of limiting).
'under' means one lot of letters go next to another.
'president' becomes 'Abe' (Abraham (Abe) Lincoln).
'r'+'ration'='rration'
'rration' put after 'abe' is 'ABERRATION'.
'is' acts as a link.
(Other definitions for aberration that I've seen before include "Mental lapse" , "Deviation from the accepted norm" , "Unwelcome deviation from normal" , "departure from normal" , "Wandering" .)