HQ designed without a cellar (8)
I believe the answer is:
basement
'cellar' is the definition.
(both can mean the space underneath a house)
'hq designed without a' is the wordplay.
'hq' becomes 'base' (I've seen this before).
'designed' becomes 'meant' (I've seen this before).
'without' is a deletion indicator.
'meant' with 'a' taken away is 'ment'.
'base'+'ment'='BASEMENT'
(Other definitions for basement that I've seen before include "Underground room" , "Floor below ground level" , "rock formation" , "Lowest floor of a building" , "underground construction" .)