Being Irish, is popularly called Red (6)

I believe the answer is:

setter

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'being' is the definition.
The definition and answer can be both animals as well as being singular nouns.
Perhaps they are linked in a way I don't understand?

I can't explain the rest of the clue.

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(Other definitions for setter that I've seen before include "Jelly, perhaps" , "Late evening sun is a" , "Dog found in street" , "Puzzle creator" , "Crossword composer" .)

I've seen this clue in the Evening Standard.

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