Storage facility set up outside back of arena (3)
I believe the answer is:
vat
'storage facility' is the definition.
(type of container)
'set up outside back of arena' is the wordplay.
'set' becomes 'tv' (TV set).
'up' shows that the letters should be reversed in order (in down clue: letters go upwards).
'outside' means one lot of letters goes inside another.
'back of' says to take the final letters.
The last letter of 'arena' is 'a'.
'tv' backwards is 'vt'.
'vt' going around 'a' is 'VAT'.
(Other definitions for vat that I've seen before include "possible source of liquid" , "Large container for liquid" , "Large tub; tax" , "Liquid storage receptacle" , "A tax on a large container?" .)