End of testing finished head teacher (9)
I believe the answer is:
governess
'teacher' is the definition.
(I know that governess is a type of teacher)
'end of testing finished head' is the wordplay.
'end of' indicates one should take the final letters.
'finished' becomes 'over' (over can mean finished or ended).
'head' becomes 'ness' (type of geographical point).
The final letter of 'testing' is 'g'.
'g'+'over'+'ness'='GOVERNESS'
(Other definitions for governess that I've seen before include "Supernanny?" , "Mary Poppins, perhaps" , "Becky Sharp, say" , "Duenna" , "Teacher" .)