Surrey town that is to inflict corporal punishment on school principal (11)
I believe the answer is:
leatherhead
'surrey town that is to inflict' is the definition.
'leatherhead' can be an answer for 'surrey town' (I've seen this before). I am not certain of the rest of the definition.
'corporal punishment on school principal' is the wordplay.
'corporal punishment' becomes 'leather' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'on' is a charade indicator (letters next to each other) (in a down clue, letters appear on others).
'school principal' becomes 'head' (synonyms).
'leather'+'head'='LEATHERHEAD'
Can you help me to learn more?
(Other definitions for leatherhead that I've seen before include "Bird from down under" , "Surrey town" .)