Sounds like Hemingway is serious (7)
I believe the answer is:
earnest
'serious' is the definition.
(similar in meaning)
'sounds like hemingway' is the wordplay.
'sounds like' shows a homophone (sound like).
'hemingway' becomes 'ernest' (author Ernest Hemingway).
'ernest' sounds like 'EARNEST'.
'is' acts as a link.
(Other definitions for earnest that I've seen before include "Sincere, solemn" , "'Serious, sincere (7)'" , "Serious - money deposit" , "money involved in contract" , "Serious; down-payment" .)