Insect gives listener a hairpiece (6)
I believe the answer is:
earwig
'insect' is the definition.
(I know that earwig is a type of insect)
'listener a hairpiece' is the wordplay.
'listener' becomes 'ear' (body part which hears or listens).
'a hairpiece' becomes 'wig' (wig is a kind of hairpiece).
'ear'+'wig'='EARWIG'
'gives' is the link.
(Other definitions for earwig that I've seen before include "Go in for eavesdropping" , "Common garden insect" , "Insect with pincer-like tail" , "One little creature" , "Insect with large rear pincers" .)