Girl with a new angle (6)
I believe the answer is:
angela
'girl' is the definition.
'with a new angle' is the wordplay.
'with' says to put letters next to each other.
'new' is an anagram indicator.
'angle' anagrammed gives 'ngela'.
'a'+'ngela' is 'ANGELA'.
(Other definitions for angela that I've seen before include "------ Gheorghiu, diva" , "-- Merkel, German Chancellor" , "Frau Merkel" , ". . . Lansbury (actress)" , "woman" .)