Cheese with fine character from Greece (4)
I believe the answer is:
feta
'cheese' is the definition.
(I've seen this before)
'fine character from greece' is the wordplay.
I cannot quite see how this works, but
'fine' could be 'f' (abbreviation) and 'f' is present in the answer.
'character' could be 'eta' (letter of the Greek alphabet) and 'eta' is present in the answer.
This accounts for all the letters.
This explanation may well be incorrect...
'with' is the link.
Can you help me to learn more?
(Other definitions for feta that I've seen before include "Goat's or sheep's milk cheese" , "Greek 8 across" , "food there" , "Greek salad cheese" , "10 down cheese" .)