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 tell whether it can be defined by this definition.

'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 present in the answer.
The remaining letters 'greater' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...

'of' acts as a link.

Can you help me to learn more?