Father had potato cooked immediately (2,3,4,2,1,3)
I believe the answer is:
at the drop of a hat
'immediately' is the definition.
(I've seen this in another clue)
'father had potato cooked' is the wordplay.
'cooked' indicates anagramming the letters (letters cooked into a new form).
'father'+'had'+'potato'='fatherhadpotato'
'fatherhadpotato' with letters rearranged gives 'AT THE DROP OF A HAT'.
(Other definitions for at the drop of a hat that I've seen before include "sudden" , "When pork pie downed" , "Immediately" , "without good reason?" , "When a tile descends" .)