Accomplished Greek character with first woman in trailer (8)
I believe the answer is:
achieved
'accomplished' is the definition.
('achieve' can be a synonym of 'accomplish')
'greek character with first woman in trailer' is the wordplay.
'greek character' becomes 'chi' (letter from the Greek alphabet**).
'with' means one lot of letters go next to another.
'first woman' becomes 'eve' (I've seen this before).
'in' indicates putting letters inside.
'trailer' becomes 'ad' (I've seen this in other clues).
'chi'+'eve'='chieve'
'chieve' placed within 'ad' is 'ACHIEVED'.
(Other definitions for achieved that I've seen before include "Attained, succeeded" , "Gained with effort" , "Attained, got there" , "executed" , "obtained" .)