Insect of annoying nature (4)
I believe the answer is:
gnat
'insect' is the definition.
(gnat is a kind of insect)
'of annoying nature' is the wordplay.
'of' says the answer is hidden in the clue.
'GNAT' can be found hidden inside 'annoying nature'.
(Other definitions for gnat that I've seen before include "mozzie" , "Something that bites" , "Small, swarming insect" , "Small (swarming) fly" , "Small biter" .)