Greek character, very loud, having shown the way, is to be toned down (7)
I believe the answer is:
muffled
'toned down' is the definition.
('muffle' can be a synonym of 'tone down')
'greek character very loud having shown the way' is the wordplay.
'greek character' becomes 'mu' (letter from the Greek alphabet**).
'very loud' becomes 'ff' (musical abbreviation).
'having' means one lot of letters go next to another.
'shown the way' becomes 'led' (I've seen this in other clues).
'mu'+'ff'+'led'='MUFFLED'
'is to be' is the link.
(Other definitions for muffled that I've seen before include "Wrapped for warmth" , "Of sound, deadened or made indistinct" , "Wrapped (up), stifled" , "Silenced; wrapped" .)