Veto old and new President (5)
I believe the answer is:
nixon
'president' is the definition.
(Richard Nixon)
'veto old and new' is the wordplay.
'veto' becomes 'nix' (I've seen this in another clue).
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'and' means one lot of letters go next to another.
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'nix'+'o'+'n'='NIXON'
(Other definitions for nixon that I've seen before include "US president, d.1994" , "37th US President" , "Politician" , "US president - subject of an opera by John Adams" , "37th president of the United States, resigned 1974" .)