President with nothing doing! (5)
I believe the answer is:
nixon
'president' is the definition.
(Richard Nixon)
'with nothing doing' is the wordplay.
'with' says to put letters next to each other.
'nothing' becomes 'nix' ('nix' can be a synonym of 'zero').
'doing' becomes 'on' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'nix' put next to 'on' is 'NIXON'.
Can you help me to learn more?
(Other definitions for nixon that I've seen before include "Only US president to have resigned from office" , "Richard -, US president who resigned in nineteen seventy four" , "Former US president" , "Watergate was his downfall" , "37th US President" .)