Slav with yen to devour very mature cheese (4,5)
I believe the answer is:
sage derby
'cheese' is the definition.
(I've seen this before)
'slav with yen to devour very mature' is the wordplay.
'slav' becomes 'serb' (I've seen this in another clue).
'with' is a charade indicator (letters next to each other).
'yen' becomes 'y' (resembles the symbol for the currency of Japan).
'to devour' means one lot of letters goes inside another (inserted letters are swallowed or devoured).
'very mature' becomes 'aged' (elderly).
'serb'+'y'='serby'
'serby' placed around 'aged' is 'SAGE DERBY'.
(Other definitions for sage derby that I've seen before include "Greenish cheese" , "Food" , "Cheese made with herb" , "Green-veined cheese" .)