Remained dignified on the radio (6)
I believe the answer is:
stayed
'remained' is the definition.
(staying is a kind of remaining)
'dignified on the radio' is the wordplay.
'dignified' becomes 'staid' (I've seen this in another clue).
'on the radio' indicates a 'sounds like' (homophone) clue.
'staid' is a homophone of 'STAYED'.
(Other definitions for stayed that I've seen before include "Secured; remained" , "Stuck around" , "Withheld; remained" , "Remained in the same place" , "having support" .)