Could Midge tolerate pet hate? (7)

I believe the answer is:

bugbear

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'pet hate?' is the definition.
(I've seen this before)

'could midge tolerate' is the wordplay.
'could midge' becomes 'bug' (I am not sure about this - if you are sure you should believe this answer much more).
'tolerate' becomes 'bear' (synonyms).
'bug'+'bear'='BUGBEAR'

Can you help me to learn more?

(Other definitions for bugbear that I've seen before include "Cause of obsessive fear" , "something terrible" , "One's special fear" , "Cause of annoyance, fear" , "Cause of irritation" .)

I've seen this clue in the Sydney Morning Herald.

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