Great many supporting Labour up in vote (6)
I believe the answer is:
ballot
'vote' is the definition.
(synonyms)
'great many supporting labour up' is the wordplay.
'great many supporting' becomes 'tol' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'labour' becomes 'lab' (abbreviation).
'up' is a reversal indicator (in down clue: letters go upwards).
'tol'+'lab'='tollab'
'tollab' back-to-front is 'BALLOT'.
'in' is the link.
Can you help me to learn more?
(Other definitions for ballot that I've seen before include "Election" , "Secret vote" , "Lottery to allocate (tickets) among applicants" , "Lottery (eg, for tickets)" , "Referendum" .)