Writer outside extremely smart restaurant (6)
I believe the answer is:
bistro
'restaurant' is the definition.
(I know that bistro is a type of restaurant)
'writer outside extremely smart' is the wordplay.
'writer' becomes 'biro' (type of pen, something which writes).
'outside' indicates putting letters inside.
'extremely' means to remove the middle letters (extreme, outside letters only).
'smart' with its centre taken out is 'st'.
'biro' going around 'st' is 'BISTRO'.
(Other definitions for bistro that I've seen before include "Small informal French restaurant" , "A small informal restaurant from France" , "Small bar-cum-restaurant" , "Cafe bar" , "Cheap restaurant" .)