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 wordplay.
'after' is a charade indicator (letters next to each other).
'awful experience' becomes 'hell'.
'dad' becomes 'father' (I've seen this before).
'takes on' is an insertion indicator.
'new' is an anagram indicator.
'role' is an anagram of 'orle'.
'father' going around 'orle' is 'forleather'.
'hell' put next to 'forleather' is 'HELL-FOR-LEATHER'.
(Other definitions for hell for leather that I've seen before include "swiftly", "without respite", "very quickly", "extremely fast" and "at great speed".)