Dog to exist with a brief depression (6)
I believe the answer is:
beagle
'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" .)