Class project supported by headteacher at the halfway point (5)
I believe the answer is:
caste
'class' is the definition.
(caste is a kind of class)
'project supported by headteacher at the halfway point' is the wordplay.
I cannot quite understand how this works, but
'project' could be 'cast' ('cast' can be a synonym of 'project') and 'cast' is located in the answer.
'point' could be 'e' (E is an example) and 'e' is present in the answer.
No letters remain.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for caste that I've seen before include "Social order" , "Hereditary Hindu social division" , "Social class or rank" , "Social group in India" , "Persons with class" .)