Flesh going off in storage space (5)
I believe the answer is:
shelf
'storage space' is the definition.
'flesh going off' is the wordplay.
'going off' indicates an anagram.
'flesh' with letters rearranged gives 'SHELF'.
'in' is the link.
(Other definitions for shelf that I've seen before include "Projecting layer of rock" , "Flat surface for holding objects" , "Sill" , "Whereon 2 down is not!" , "Storage ledge" .)