One slip ruined Greek character (7)
I believe the answer is:
epsilon
'greek character' is the definition.
(letter from the Greek alphabet)
'one slip ruined' is the wordplay.
'ruined' indicates anagramming the letters.
'one'+'slip'='oneslip'
'oneslip' with letters rearranged gives 'EPSILON'.
(Other definitions for epsilon that I've seen before include "5th letter of the Greek alphabet" , "character in Greece" , "Greek short E" , "Greek letter - pinoles (anag)" , "Fifth brightest star in a constellation" .)