Denizen briefly entangled in plot, gaudily dressed (9)

'gaudily dressed' is the definition.
(to bedizen is to dress gaudily)

'denizen briefly entangled in plot' is the wordplay.
'briefly' means to remove the last letter.
'entangled' indicates an anagram.
'in' means one lot of letters goes inside another.
'plot' becomes 'bed' (bed is a kind of plot).
'denizen' with its last letter taken off is 'denize'.
'denize' anagrammed gives 'dizene'.
'dizene' placed within 'bed' is 'BEDIZENED'.