Cockney is not on English course (7)
I believe the answer is:
aintree
'course' is the definition.
(I've seen this before)
'cockney is not on english' is the wordplay.
'cockney' becomes 're' (I am not sure about this - if you are sure you should believe this answer much more).
'is not' becomes 'ain't' ('ain't' is a non-standard form of 'isn't').
'on' means one lot of letters go next to another.
'english' becomes 'E' (abbreviation as in OED).
're' after 'aint' is 'aintre'.
'aintre'+'e'='AINTREE'
Can you help me to learn more?
(Other definitions for aintree that I've seen before include "Trainee in Grand National venue" , "Here they run" , "place for horse racing" , "Home of the Grand National" , "Liverpool's racecourse" .)