Restaurant where Spooner's woman to come first (3,4)
I believe the answer is:
tea shop
'restaurant' is the definition.
(tea shop is a kind of restaurant)
I can't explain the rest of the clue.
(Other definitions for tea shop that I've seen before include "Cafe (paradoxically?)" , "Restaurant serving light meals" , "Small cafe" , "refreshing facility" , "Refreshments provider" .)