Reportedly remained sober (5)
I believe the answer is:
staid
'sober' is the definition.
(synonyms)
'reportedly remained' is the wordplay.
'reportedly' shows a homophone (sound like).
'remained' becomes 'stayed' ('stay' can be a synonym of 'remain').
'stayed' sounds like 'STAID'.
(Other definitions for staid that I've seen before include "Sober, grave" , "Stuffy, traditional" , "Proper; sedate" , "Very conventional and dull" , "Conventional (character)" .)