Perhaps Miss America has drink with the Queen before her round (9)
I believe the answer is:
superhero
'perhaps miss america' is the definition.
(I know that Miss America is a superhero)
'with the queen before her round' is the wordplay.
'with' means one lot of letters go next to another.
'the queen before' becomes 'super' (I can't explain this - if you can you should give a lot more credence to this answer).
'round' becomes 'o' (round can mean a round object).
'super' put next to 'her' is 'superher'.
'superher'+'o'='SUPERHERO'
'has drink' acts as a link.
This may not be right. Some or all of it may be part of another bit of the clue.
(Other definitions for superhero that I've seen before include "Batman, say?" , "One possibly involved in saving" , "I'm often seen in a cape" , "really great guy" , "Her poseur (anag.)" .)