Fake half of dog's hair cleaner (7)
I believe the answer is:
shampoo
'hair cleaner' is the definition.
(I've seen this in another clue)
'fake half of dog's' is the wordplay.
'fake' becomes 'sham' (sham can mean fake or pretend).
'half of' suggests halving the letters.
'dog' becomes 'poodle' (breed of dog).
'poodle' with half the letters taken is 'poo'.
'sham'+'poo'='SHAMPOO'
(Other definitions for shampoo that I've seen before include "Would Mao shop for this cleaner?" , "Hair cleanser" , "Hair-cleaner" , "Hair or carpet cleaner" , "treat shock?" .)