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)
'the dog is coming up' is the wordplay.
'the dog' becomes 'pom' (I've seen this before).
'is coming up' is a reversal indicator.
'pom' in reverse letter order is 'MOP'.
'of' 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" .)