Ask for quiet work in retail outlet (4)
I believe the answer is:
shop
'retail outlet' is the definition.
(I know that retail outlet can be written as shop)
'ask for quiet work' is the wordplay.
'ask for quiet' becomes 'sh' (to sh someone is to ask them to be quiet).
'work' becomes 'op' (operation, work done in an operating theatre).
'sh'+'op'='SHOP'
'in' is the link.
(Other definitions for shop that I've seen before include "Store or boutique" , "Make purchase; inform on (someone)" , "sales outlet" , "Sell" , "Posh (anag.)" .)