Kay loses the head with Herb in the doghouse (6)

I believe the answer is:

kennel

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'doghouse' is the definition.
('kennel' can be a synonym of 'doghouse')

I don't understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for kennel that I've seen before include "Dog's shelter" , "Dog's abode" , "Dog house" , "housing for boxer, say" , "Doghouse" .)

I've seen this clue in the Irish Times.

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