Cover over open-air pool (4)
I believe the answer is:
lido
'open-air pool' is the definition.
(I've seen this before)
'cover over' is the wordplay.
'cover' becomes 'lid' (lid is a kind of cover).
'over' becomes 'o' (cricket abbreviation).
'lid'+'o'='LIDO'
(Other definitions for lido that I've seen before include "Public open swimming pool" , "Aquatic leisure centre" , "Open-air swimming-pool" , "Public bathing beach" , "Swimming and leisure area" .)