Greek character's ten cheers (4)
I believe the answer is:
iota
'greek character's' is the definition.
(letter from the Greek alphabet)
'ten cheers' is the wordplay.
'ten' becomes 'io'.
'cheers' becomes 'ta' (I've seen this in other clues).
'io'+'ta'='IOTA'
(Other definitions for iota that I've seen before include "Greek letter of little value" , "(Not one) little bit" , "Trace" , "Old letter" , "Smidgen" .)