Party backed great number in vote (6)
I believe the answer is:
ballot
'vote' is the definition.
(balloting is a kind of voting)
'party backed great number' is the wordplay.
'party' becomes 'ball' (ball is a kind of party).
'backed' is a reversal indicator.
'great number' becomes 'to' (I am not sure about this - if you are sure you should believe this answer much more).
'to' written backwards gives 'ot'.
'ball'+'ot'='BALLOT'
'in' acts as a link.
Can you help me to learn more?
(Other definitions for ballot that I've seen before include "Voting procedure" , "Document listing the alternatives to vote for" , "Single or collective vote" , "Plebiscite" , "Referendum" .)