Subdued Greek character heads for the emergency department (5)
I believe the answer is:
muted
'subdued' is the definition.
(both can mean restrained or subtle)
'greek character heads for the emergency department' is the wordplay.
'greek character' becomes 'mu' (letter from the Greek alphabet).
'heads for' indicates taking the first letters.
The initial letters of 'the emergency department' is 'ted'.
'mu'+'ted'='MUTED'
(Other definitions for muted that I've seen before include "In a softened tone" , "Of great weight" , "In music, with sound deadened or muffled" , "Subdued; not bright" , "Quietened" .)