Remained sober, reportedly (6)
I believe the answer is:
stayed
'remained' is the definition.
(staying is a kind of remaining)
'sober reportedly' is the wordplay.
'sober' becomes 'staid' (synonyms).
'reportedly' shows a homophone (sound like).
'staid' sounds like 'STAYED'.
(Other definitions for stayed that I've seen before include "Supported" , "Remained; guyed" , "Remained in the same place" , "Remained or posponed" , "Didn't go" .)