Using every effort to fault supply (4,3)
I believe the answer is:
flat out
'using every effort' is the definition.
(I've seen this before)
'to fault supply' is the wordplay.
'supply' is an anagram indicator (in a supple way).
'to'+'fault'='tofault'
'tofault' with letters rearranged gives 'FLAT OUT'.
(Other definitions for flat out that I've seen before include "Lying on floor" , "Bluntly" , "Using every effort" , "very quickly?" , "At top speed - totally exhausted" .)