Choose to speak for everyone on the register (10)
I believe the answer is:
'everyone on the register' is the definition.
(everyone on the electoral roll)
'choose to speak' is the wordplay.
'choose' becomes 'elect' (electing is a kind of choosing).
'to speak' becomes 'orate' (orating is a kind of speaking).
'for' is the link.
(Other definitions for electorate that I've seen before include "Voters as a whole" , "choosing body" , "Constituency" , "Everyone choosing" , "Voters in general" .)