President's bottom, bottom President (5)
I believe the answer is:
trump
'president' is the definition.
(Donald Trump)
'president's bottom bottom' is the wordplay.
'bottom' says to take the final letters.
'bottom' becomes 'rump' ('rump' can be a synonym of 'bottom'**).
The last letter of 'president' is 't'.
't'+'rump'='TRUMP'
(Other definitions for trump that I've seen before include "This card has an advantage" , "Outdo (with a card?)" , "Card beating other suits" , "Valuable card" , "High-ranking card" .)