Flirt’s game, drawing out Romeo (6)
I believe the answer is:
coquet
'flirt's' is the definition.
(synonyms)
'game drawing out romeo' is the wordplay.
'game' becomes 'croquet' (croquet is a kind of game).
'drawing out' suggests deleting specific letters.
'romeo' becomes 'r' (phonetic alphabet: alpha, bravo, charlie etc.).
'croquet' with 'r' taken away is 'COQUET'.
(Other definitions for coquet that I've seen before include "Behave flirtatiously" , "Flirt" .)