Determined to broadcast Hemingway, for example (7)
I believe the answer is:
earnest
'determined' is the definition.
(I've seen this before)
'broadcast hemingway for example' is the wordplay.
'broadcast' indicates a 'sounds like' (homophone) clue (how the word might sound on the radio or TV).
'hemingway for example' becomes 'ernest' (Ernest Hemingway).
'ernest' is a homophone of 'EARNEST'.
'to' is the link.
(Other definitions for earnest that I've seen before include "money involved in contract" , "Serious in intention" , "Serious, intent" , "businesslike" , "Grave" .)