Sort of girl that's grave with zero yen (6)
I believe the answer is:
tomboy
'sort of girl' is the definition.
'grave with zero yen' is the wordplay.
'grave' becomes 'tomb' ('tomb' can be a synonym of 'grave').
'with' says to put letters next to each other.
'zero' becomes 'o'.
'yen' becomes 'y'.
'tomb'+'o'+'y'='TOMBOY'
'that's' is the link.
(Other definitions for tomboy that I've seen before include "Girl dressed in a masculine manner" , "Girl with the character of a lad" , "Girl in trousers, perhaps?" , "Girl who likes rough and noisy activities" , "girl behaving boisterously" .)