Cool-headed girl with superior quality (5)
I believe the answer is:
class
'superior quality' is the definition.
'class' can be an answer for 'quality' (class is a kind of quality). I'm not certain of the 'superior' bit.
'cool-headed girl' is the wordplay.
'cool-headed' becomes 'c' (this might be a standard abbreviation of which I'm unaware).
'girl' becomes 'lass' (lass can informally mean a girl).
'c'+'lass'='CLASS'
'with' acts as a link.
Can you help me to learn more?
(Other definitions for class that I've seen before include "School form" , "Order - quality" , "First-rate" , "Type; social level" , "Teaching group" .)