Cause of annoyance is biting insect on wild animal (7)
I believe the answer is:
bugbear
'cause of annoyance' is the definition.
'bugbear' can be an answer for 'annoyance' (I've seen this before). I am not certain of the 'cause of' bit.
'biting insect on wild animal' is the wordplay.
'biting insect' becomes 'bug' (bug is a kind of insect. I am not sure about the 'biting' bit.).
'on' says to put letters next to each other (in a down clue, letters appear on others).
'wild animal' becomes 'bear' (bears are wild animals).
'bug'+'bear'='BUGBEAR'
'is' acts as a link.
Can you help me to learn more?
(Other definitions for bugbear that I've seen before include "bogeyman" , "constant worry" , "Cause of annoyance, fear" , "An object of terror, dislike or annoyance" , "It causes obsessive fear" .)