Society girl at first turns on Romeo — one owing money (6)
I believe the answer is:
debtor
'one owing money' is the definition.
(I've seen this before)
'society girl at first turns on romeo' is the wordplay.
'society girl' becomes 'deb' (I've seen this before).
'at first' indicates taking the first letters.
The initial letters of 'turns on romeo' is 'tor'.
'deb'+'tor'='DEBTOR'
(Other definitions for debtor that I've seen before include "Person owing money" , "Opposite of creditor" , "Anyone owing money" , "One owing money" , "Borrower" .)