Sauce quickly runs out (5)
I believe the answer is:
pesto
'sauce' is the definition.
(I've seen this before)
'quickly runs out' is the wordplay.
'quickly' becomes 'presto' (I've seen this before).
'runs' becomes 'r' (cricket abbreviation).
'out' suggests deleting specific letters.
'presto' with 'r' removed is 'PESTO'.
(Other definitions for pesto that I've seen before include "Pasta sauce variety" , "Ligurian food" , "Sauce of basil, pine nuts and garlic" , "Green sauce" , "Sauce of basil, pine nuts, etc" .)