Crossword Genius

Dog to exist with a brief depression (6)

Ross

I believe the answer is:

beagle

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'dog' is the definition.
(I know that beagle is a type of dog)

'exist with a brief depression' is the wordplay.
'exist with' becomes 'bea' (I can't justify this - if you can you should believe this answer much more).
'a brief' means to remove the last letter (a shorter or briefer version of the word).
'depression' becomes 'glen' (glen is a kind of depression).
'glen' with its last letter removed is 'gle'.
'bea'+'gle'='BEAGLE'

'to' acts as a link.

Can you help me to learn more?

(Other definitions for beagle that I've seen before include "Darwin voyaged in this ship" , "Small hunting dog" , "Breed of dog in a glebe" , "Hound dog" , "Type of hound" .)

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