Flamboyant Queen embraced by graduate and libertine (7)
I believe the answer is:
baroque
'flamboyant' is the definition.
(thesaurus)
'queen embraced by graduate and libertine' is the wordplay.
'queen' becomes 'q' (abbreviation used in chess).
'embraced by' indicates putting letters inside.
'graduate' becomes 'ba'.
'and' is a charade indicator (letters next to each other).
'libertine' becomes 'roue' (roue is a kind of libertine).
'ba'+'roue'='baroue'
'q' put into 'baroue' is 'BAROQUE'.
(Other definitions for baroque that I've seen before include "Style of e.g. Wren, Bach" , "With elaborate ornamentation" , "Extravagantly ornate" , "Highly ornate in style" , "Elaborate style" .)