Woman debuts in Paris and Milan (3)
I believe the answer is:
pam
'woman' is the definition.
'debuts in paris and milan' is the wordplay.
'debuts in' suggests taking the first letters (I've seen 'debut in' mean this).
The first letters of 'paris and milan' is 'PAM'.
(Other definitions for pam that I've seen before include "- Ayres, English poet" , "Short girl's name" , "Female" .)