New store keeps British ice-cream (6)
I believe the answer is:
sorbet
'ice-cream' is the definition.
'new store keeps british' is the wordplay.
'new' indicates an anagram.
'keeps' indicates putting letters inside.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'store' anagrammed gives 'soret'.
'soret' enclosing 'b' is 'SORBET'.
(Other definitions for sorbet that I've seen before include "Sweet" , "Fruit water-ice" , "Water ice dessert" , "Frozen dessert" , "Fruit juice and water ice" .)