Hawk pursues a large female retreating as fast as possible (4,3)
I believe the answer is:
flat out
'as fast as possible' is the definition.
(I've seen this before)
'hawk pursues a large female retreating' is the wordplay.
'hawk' becomes 'tout' (I've seen this in another clue).
'pursues' is a charade indicator (letters next to each other).
'large' becomes 'L' (eg in clothes sizes).
'female' becomes 'f' (common abbreviation).
'retreating' shows that the letters should be reversed in order.
'a'+'l'+'f'='alf'
'alf' reversed gives 'fla'.
'tout' after 'fla' is 'FLAT OUT'.
(Other definitions for flat out that I've seen before include "Lying on floor" , "As fast as possible" , "KO'd" , "Using every effort" , "Exhausted - at full speed" .)