Cool display from school head (15)
I believe the answer is:
standoffishness
'cool display from school head' is the definition.
The definition and answer can be both human attributes as well as being singular nouns.
Maybe there's a link between them I don't understand?
'cool display from school head' is the wordplay.
'cool' becomes 'standoffish' (I've seen this before).
'display from school head' becomes 'ness' (I can't justify this - if you can you should believe this answer much more).
'standoffish'+'ness'='STANDOFFISHNESS'
Can you help me to learn more?
(Other definitions for standoffishness that I've seen before include "Remote nature" , "Detachment" .)