Beautiful woman's demand for attention - say you are engaged! (5)
I believe the answer is:
houri
'beautiful woman's' is the definition.
(beautiful woman in paradise in Islam)
'demand for attention say you are engaged' is the wordplay.
'demand for attention' becomes 'hoi' (sound for getting someone's attention).
'say you' becomes 'ur' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'are engaged' indicates putting letters inside (inserted letters are taken in or engaged).
'hoi' enclosing 'ur' is 'HOURI'.
(Other definitions for houri that I've seen before include "Voluptuously alluring woman" , "Paradisal nymph" , "Young beautiful woman of the Moslem Paradise" , "Virgin companion of the Muslim faithful in Paradise" , "faithful female companion" .)