As expressed in Greek, unlimited fame (6)
I believe the answer is:
repute
'fame' is the definition.
(repute can mean fame or reputation)
'as expressed in greek unlimited' is the wordplay.
'as expressed' becomes 'put' (I've seen this in another clue. I am not sure about the 'as' bit.).
'in' means one lot of letters goes inside another.
'unlimited' says to take the centre (discard the edges or 'limits' of the word).
The middle letters of 'greek' are 'ree'.
'put' going inside 'ree' is 'REPUTE'.
(Other definitions for repute that I've seen before include "State of high regard" , "Public standing" , "Public estimation" , "Generally held opinion" , "Celebrity, renown" .)