Party debut for miss in old cloak (6)
I believe the answer is:
domino
'miss in old cloak' is the definition.
'domino' can be an answer for 'cloak' (domino is a kind of cloak). I'm unsure of the 'miss in old' bit.
'party debut' is the wordplay.
'party' becomes 'do' (do is a kind of party).
'debut' becomes 'mino' (I can't justify this - if you can you should give a lot more credence to this answer).
'do'+'mino'='DOMINO'
'for' acts as a link.
Can you help me to learn more?
(Other definitions for domino that I've seen before include "such a falling effect" , "Cloak for masquerading - in mood (anag)" , "Playing piece with spots" , "Spotted playing tile" , "One falls, all fall" .)