Bill runs out of crack (4)
I believe the answer is:
beak
'bill' is the definition.
('beak' can be a synonym of 'bill')
'runs out of crack' is the wordplay.
'runs' becomes 'r' (cricket abbreviation).
'out of' is a deletion indicator.
'crack' becomes 'break'.
'break' with 'r' removed is 'BEAK'.
(Other definitions for beak that I've seen before include "Bird's mouth" , "Schoolmarm" , "Horny mouth of a bird" , "Bill; nose" , "Bird's bill" .)