Insect has hair, not its own, on part of head (6)
I believe the answer is:
earwig
'insect' is the definition.
(I know that earwig is a type of insect)
'hair not its own on part of head' is the wordplay.
'hair not its own' becomes 'wig' (fake hair).
'on' means one lot of letters go next to another.
'part of head' becomes 'ear' (ears are part of the head).
'wig' after 'ear' is 'EARWIG'.
'has' is the link.
(Other definitions for earwig that I've seen before include "An insect, I wager (anag.)" , "A bug for Americans" , "Creepy type" , "Common garden insect" , "court" .)