Crossword Genius

Pet with a supportive mistress (6)

Ross

I believe the answer is:

lapdog

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This could be a double definition.

'pet' is the first definition.
(I know that lapdog is a type of dog)

'supportive mistress' is the second definition.
Although both the answer and definition are singular nouns, I cannot understand how they can define each other.

'with a' is the link.

Can you help me to learn more?

(Other definitions for lapdog that I've seen before include "little pet" , "lackey" , "one of man's more diminutive best friends" , "Pom, for one" , "Submissive type" .)

I've seen this clue in the Evening Standard.
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