Remained sober, say (6)
I believe the answer is:
stayed
'remained' is the definition.
(staying is a kind of remaining)
'sober say' is the wordplay.
'sober' becomes 'staid' ('staid' can be a synonym of 'sober').
'say' shows a homophone (sound like).
'staid' sounds like 'STAYED'.
(Other definitions for stayed that I've seen before include "Secured; remained" , "Remained or posponed" , "Tarried" , "Remained, propped up" , "Withheld; remained" .)