Cover on old pool (4)
I believe the answer is:
lido
'pool' is the definition.
(I've seen this before)
'cover on old' is the wordplay.
'cover' becomes 'lid' (lid is a kind of cover).
'on' means one lot of letters go next to another (in a down clue, letters appear on others).
'old' becomes 'o' (abbreviation).
'lid'+'o'='LIDO'
(Other definitions for lido that I've seen before include "Swimming and leisure area" , "Bathing pool" , "bathing facilities" , "---- di Jesolo, Italian Adriatic resort" , "Swim here" .)