Remained solemn in conversation (6)
I believe the answer is:
stayed
'remained' is the definition.
(staying is a kind of remaining)
'solemn in conversation' is the wordplay.
'solemn' becomes 'staid' (both can mean serious).
'in conversation' shows a homophone (sound like).
'staid' sounds like 'STAYED'.
(Other definitions for stayed that I've seen before include "Supported" , "Hung about" , "Didn't go" , "Remained; steadied" , "Remained, did not leave" .)