Bullish sign (not half) in Greek character (3)
I believe the answer is:
tau
'greek character' is the definition.
(letter from the Greek alphabet)
'bullish sign not half' is the wordplay.
'bullish sign' becomes 'ta' (I am not sure about this - if you are sure you should believe this answer much more).
'not' becomes 'un' (I've seen this in other clues).
'half' means to take half the letters.
'un' cut in half is 'u'.
'ta'+'u'='TAU'
'in' is the link.
(Other definitions for tau that I've seen before include "19th letter of the Greek alphabet" , "Marathon character" , "Greek letter; cross" , "character from Athens" , "A subatomic particle" .)