Strict new school for Cockneys (6)
I believe the answer is:
narrow
'strict' is the definition.
(narrow can mean strict or precise)
'new school for cockneys' is the wordplay.
I cannot really understand how this works, but
'new' could be 'n' (common abbreviation eg NT for New Testament) and 'n' is present in the answer.
The remaining letters 'arrow' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for narrow that I've seen before include "Thin; taper" , "Restricted in width." , "Strict" , "Strait or thin" , "Become restricted" .)