What the majority of bit players would like? (7,4)

'what the majority' is the definition.
I know nothing about this answer so I can't judge whether this works.

'bit players would like?' is the wordplay.
I cannot really see how this works, but
'bit' could be 'part' (both can mean a piece of something) and 'part' is found in the answer.
The remaining letters 'greater' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).

'of' is the link.

Can you help me to learn more?