Insect having an insect's tail (3)
I believe the answer is:
ant
'insect' is the definition.
(ant is a kind of insect)
'an insect's tail' is the wordplay.
'an insect's' becomes 'ants' (ant is a kind of insect).
'tail' means to remove the last letter (I've seen 'tailed' mean this (to tail something can mean to remove its end)).
'ants' with its final letter removed is 'ANT'.
'having' is the link.
(Other definitions for ant that I've seen before include "Industrious insect" , "Proverbially hard-working insect" , "Emmet or pismire" , "Small busy insect" , "Worker on the hill" .)