Unfinished prestige store (5)
I believe the answer is:
cache
'store' is the definition.
(cache is a kind of store)
'unfinished prestige' is the wordplay.
'unfinished' means to remove the last letter.
'prestige' becomes 'cachet' ('cachet' can be a synonym of 'prestige').
'cachet' with its final letter removed is 'CACHE'.
(Other definitions for cache that I've seen before include "Hiding place for treasure etc" , "Conceal" , "Something hidden" , "(Place in) hidden store" , "Secret hiding place" .)