After awful experience Dad takes on new role extremely quickly (4,3,7)
I believe the answer is:
hell for leather
Here is my best explanation:
'extremely quickly' is the definition.
'after awful experience dad takes on new role' is the subsidiary indication.
'after' is a charade indicator (letters next to each other).
'awful experience' becomes 'hell'.
'dad' becomes 'father' (**).
'takes on' indicates putting letters inside.
'new' indicates an anagram.
'role' with letters rearranged gives 'orle'.
'father' placed around 'orle' is 'forleather'.
'hell' next to 'forleather' is 'hellforleather'.