Sly look around cool street in British city (9)
I believe the answer is:
leicester
'british city' is the definition.
'leicester' can be an answer for 'city' (Leicester is an example). I am unsure of the 'british' bit.
'sly look around cool street' is the wordplay.
'sly look' becomes 'leer' (I've seen this before).
'around' is an insertion indicator.
'cool' becomes 'ice' (icing is a kind of cooling).
'street' becomes 'st'.
'ice'+'st'='icest'
'leer' going around 'icest' is 'LEICESTER'.
'in' acts as a link.
Can you help me to learn more?
(Other definitions for leicester that I've seen before include "Elizabeth the first's favourite" , "Queen's favourite" , "royal favourite" , "London film premiere location" , "English cheese, maybe red" .)