Insect on animal is a cause of annoyance (7)

I believe the answer is:

bugbear

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'cause of annoyance' is the definition.
'bugbear' can be an answer for 'annoyance' (I've seen this before). I'm not certain of the 'cause of' bit.

'insect on animal' is the wordplay.
'insect' becomes 'bug' (bug is a kind of insect).
'on animal' becomes 'bear' (bear is a kind of animal. I am not sure about the 'on' bit.).
'bug'+'bear'='BUGBEAR'

'is a' is the link.

Can you help me to learn more?

(Other definitions for bugbear that I've seen before include "A thing causing excessive anxiety" , "pet hate" , "Object of dread or apprehension" , "[BOGYMAN]" , "Cause of irritation" .)

I've seen this clue in The Globe and Mail.

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