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'm not sure about 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 believe this answer much more).
'on' says to put 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" .)