Bishop united with bird and dog (6)

I believe the answer is:

beagle

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'dog' is the definition.
(beagle is a kind of dog)

I cannot understand how the remainder of the clue works.

(Other definitions for beagle that I've seen before include "Hunting hound" , "Hound dog" , "5 [MANS BEST FRIEND]" , "Small, sturdy breed of hound" , "Short-haired dog" .)

I've seen this clue in The Mirror.

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