Store for uncut rocks and diamonds by theatre (3,5)
I believe the answer is:
ice house
'store for uncut rocks' is the definition.
(store for rocks of ice)
'diamonds by theatre' is the wordplay.
'diamonds' becomes 'ice' (slang term for diamonds).
'by' means one lot of letters go next to another.
'theatre' becomes 'house' (as in 'the best seats in the house').
'ice'+'house'='ICE-HOUSE'
'and' acts as a link.
(Other definitions for ice house that I've seen before include "Cold storage building" , "Igloo" , "Former cold store" .)