Cover over open-air swimming pool (4)
I believe the answer is:
lido
'open-air swimming pool' is the definition.
(a lido is an outdoor swimming pool)
'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 "Italian bathing place" , "Venice's beach island facing the Adriatic" , "Open-air swimming-pool" , "Swimming bath" , "Venetian resort" .)