Demo riotous in style (4)
I believe the answer is:
mode
'style' is the definition.
(synonyms)
'demo riotous' is the wordplay.
'riotous' indicates an anagram.
'demo' with letters rearranged gives 'MODE'.
'in' is the link.
(Other definitions for mode that I've seen before include "Way, method" , "Manner, style" , "Style (of clothes, etc)" , "Fashion - look" , "Fashion; manner" .)