Worthless Greek character, little good, a politician (8)
I believe the answer is:
nugatory
'worthless' is the definition.
('nugatory' can be similar in meaning to 'worthless')
'greek character little good a politician' is the wordplay.
'greek character' becomes 'nu' (letter from the Greek alphabet).
'little' indicates taking the first letters.
'politician' becomes 'tory' (I've seen this before**).
The initial letter of 'good' is 'g'.
'nu'+'g'+'a'+'tory'='NUGATORY'
(Other definitions for nugatory that I've seen before include "Insignificant or trivial" , "Worthless - trifling" , "Worthless or of no real value" , "Any grout (anag) - trifling" , "to little effect" .)