Shot Greek character and president (4)
I believe the answer is:
chip
'shot' is the definition.
(I know that chip is a type of approach)
'greek character and president' is the wordplay.
'greek character' becomes 'chi' (letter from the Greek alphabet).
'and' is a charade indicator (letters next to each other).
'president' becomes 'p' (common abbreviation eg in VP).
'chi'+'p'='CHIP'
(Other definitions for chip that I've seen before include "Damage" , "Small fragment (of potato?)" , "Shaving (found on one's shoulder?)" , "Small piece of stone or silicon" , "Piece of wood, potato, or silicon" .)