Unfinished gateau gets stored initially in container (4)
I believe the answer is:
cask
'container' is the definition.
(cask is a kind of container)
'unfinished gateau gets stored initially' is the wordplay.
'unfinished' means to remove the last letter.
'gateau' becomes 'cake' (I've seen this before).
'gets' is an insertion indicator (gets can mean captures or absorbs).
'initially' suggests taking the first letters.
The first letter of 'stored' is 's'.
'cake' with its final letter removed is 'cak'.
'cak' enclosing 's' is 'CASK'.
'in' is the link.
(Other definitions for cask that I've seen before include "Wine barrel" , "VAT?" , "Drink here" , "Beer container" , "Liquor container" .)