A bit, or piece, on the president (8)
I believe the answer is:
particle
'a bit' is the definition.
(I have seen 'Small bit ' mean 'particle' so perhaps 'bit' could also mean 'particle')
'piece on the president' is the wordplay.
I cannot quite understand how this works, but
'piece' could be 'article' (I've seen this before) and 'article' is found within the answer.
'president' could be 'p' (common abbreviation eg in VP) and 'p' is present in the answer.
No letters remain.
This may be the basis of clue (or it may be nonsense).
'or' is the link.
Can you help me to learn more?
(Other definitions for particle that I've seen before include "Fragment of matter" , "Minute fragment" , "Tiny piece of anything" , "Scrap" , "Small amount" .)