Cover old open-air pool (4)
I believe the answer is:
lido
'open-air pool' is the definition.
(I've seen this before)
'cover old' is the wordplay.
'cover' becomes 'lid' (lid is a kind of cover).
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'lid'+'o'='LIDO'
(Other definitions for lido that I've seen before include "bathing facilities" , "Aquatic leisure centre" , "Open-air swimming pool" , "Swim here" , "bathing-beach" .)