Ruder-sounding dog (7)

I believe the answer is:

courser

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'dog' is the definition.
The definition and answer can be both animals as well as being singular nouns.
Maybe you can see an association between them that I can't see?

I don't understand the rest of the clue.

Can you help me to learn more?

(Other definitions for courser that I've seen before include "Runner" , "Swift horse" , "One hunting with dogs" , "Hunter of hares - speedy horse or bird" .)

I've seen this clue in The Times.

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