The girl left an invisible emanation (5)
I believe the answer is:
laura
'the girl' is the definition.
(girl's name)
'left an invisible emanation' is the wordplay.
'left' becomes 'l' (common abbreviation).
'an invisible emanation' becomes 'aura' (I've seen this before).
'l'+'aura'='LAURA'
(Other definitions for laura that I've seen before include "1944 American film noir directed by Otto Preminger" , "- Ashley, Welsh clothes, furnishings designer" , "girl" , "Girl's name" , "Cells of a group of recluses" .)