Choice, but no starter choice (8)
I believe the answer is:
election
'choice' is the definition.
(election is a kind of choice)
'no starter choice' is the wordplay.
'no starter' means to remove the first letter.
'choice' becomes 'selection' ('selection' can be a synonym of 'choice').
'selection' with its first letter taken away is 'ELECTION'.
'but' is the link.
(Other definitions for election that I've seen before include "Public vote" , "Formal vote" , "Vote to choose representatives" , "Time to vote" , "An act of democracy" .)