Silent Greek character outside of Thule (4)
I believe the answer is:
mute
'silent' is the definition.
('mute' can be a synonym of 'silent')
'greek character outside of thule' is the wordplay.
'greek character' becomes 'mu' (letter from the Greek alphabet**).
'outside of' means to remove the middle letters.
'thule' with its centre taken out is 'te'.
'mu'+'te'='MUTE'
(Other definitions for mute that I've seen before include "Deaden sound of" , "Silent - dumb" , "Silent, refraining from speaking" , "Soften the sound" , "Unable to speak" .)