Broken person first to divulge answer (7)
I believe the answer is:
respond
'answer' is the definition.
(I know that answer can be written as respond)
'broken person first to divulge' is the wordplay.
'broken' is an anagram indicator.
'first to' suggests taking the first letters.
The initial letter of 'divulge' is 'd'.
'person' with letters rearranged gives 'respon'.
'respon'+'d'='RESPOND'
(Other definitions for respond that I've seen before include "Write back" , "State in reply" , "Answer back" , "React (positively) to a stimulus or treatment" , "Come back" .)