Sincere answer received by Hemingway? (7)
I believe the answer is:
earnest
'sincere' is the definition.
('earnest' can be similar in meaning to 'sincere')
'answer received by hemingway?' is the wordplay.
'answer' becomes 'a' (abbreviation eg in Q and A).
'received by' is an insertion indicator.
'hemingway?' becomes 'ernest' ('Ernest Hemingway' can be a synonym of 'hemingway').
'a' placed within 'ernest' is 'EARNEST'.
(Other definitions for earnest that I've seen before include "Pledge - far from frivolous" , "'Serious, sincere (7)'" , "Fixed" , "art collector" , "guarantee" .)