The hair of the dog is coming up! (3)
I believe the answer is:
mop
'the hair' is the definition.
(mop can mean a mass of hair)
'dog is coming up' is the wordplay.
'dog' becomes 'pom' (short for Pomeranian).
'is coming up' says the letters should be written in reverse (in a down clue, letters go up).
'pom' back-to-front is 'MOP'.
'of the' is the link.
(Other definitions for mop that I've seen before include "Clean; mass of hair" , "Swab" , "Floor cleaner" , "A thick mass of hair on head" , "Cleaning implement" .)