Rubbish President nearly dropping odds (8)
I believe the answer is:
trumpery
'rubbish' is the definition.
(both can mean nonsense)
'president nearly dropping odds' is the wordplay.
'president' becomes 'trump' (Donald Trump).
'dropping odds' means one should take alternating letters (the odd-numbered letters are removed).
The alternating letters of 'nearly' are 'ery'.
'trump'+'ery'='TRUMPERY'
(Other definitions for trumpery that I've seen before include "Showy but worthless articles" , "Worthless trinkets" , "Twaddle" , "rubbish" , "Worthless (thing)" .)