Greek character thus gets score? (5)
I believe the answer is:
music
'score?' is the definition.
(score is a kind of music)
'greek character thus' is the wordplay.
'greek character' becomes 'mu' (letter from the Greek alphabet).
'thus' becomes 'sic' ('sic' can be a synonym of 'thus').
'mu'+'sic'='MUSIC'
'gets' is the link.
(Other definitions for music that I've seen before include "Composer's product" , "Composed sound" , "Art form involving sound" , "'Fled is that ---: do I wake or sleep?' (Keats)" , "Crafted sound" .)