Cooling device storing large pastry dish (4)
I believe the answer is:
flan
'pastry dish' is the definition.
(I've seen this before)
'cooling device storing large' is the wordplay.
'cooling device' becomes 'fan' (I've seen this in another clue).
'storing' indicates putting letters inside.
'large' becomes 'L' (eg in clothes sizes).
'fan' going around 'l' is 'FLAN'.
(Other definitions for flan that I've seen before include "Open pastry filled with savouries, fruit or custard" , "Open pastry case with savoury filling" , "dish, sweet or savoury" , "Flat open tart" , "pudding!" .)