Potato father had mashed instantly (2,3,4,2,1,3)
I believe the answer is:
at the drop of a hat
'instantly' is the definition.
(I've seen this in another clue)
'potato father had mashed' is the wordplay.
'mashed' indicates anagramming the letters.
'potato'+'father'+'had'='potatofatherhad'
'potatofatherhad' 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 "without good reason?" , "Immediately" , "sudden" , "just like that" , "When pork pie downed" .)