Girl with unusually nice heart (9)
I believe the answer is:
catherine
'girl' is the definition.
(girl's name)
'unusually nice heart' is the wordplay.
'unusually' indicates anagramming the letters.
'nice'+'heart'='niceheart'
'niceheart' is an anagram of 'CATHERINE'.
'with' acts as a link.
(Other definitions for catherine that I've seen before include "-- Wheel; -- the Great" , "Henry's fifth" , "Female" , "A - wheel is a firework" , "Parr or Howard, say" .)