Girl soon losing love (3)
I believe the answer is:
ann
'girl' is the definition.
'soon losing love' is the wordplay.
'soon' becomes 'anon' (I've seen this before).
'losing' indicates named letters should be taken away.
'love' becomes 'o' (In tennis, 'love' means 'zero').
'anon' with 'o' removed is 'ANN'.
(Other definitions for ann that I've seen before include "Girl's name" , "- Widdecombe MP" , "eg Miss Widdecombe" , "Ms Widdecombe" , "... -Margaret (film actress)" .)