Near pool bag a finch (6)

I believe the answer is:

linnet

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'finch' is the definition.
(I know that linnet is a type of finch)

I don't understand the remainder of the clue.

(Other definitions for linnet that I've seen before include "Songbird (to 6 18)" , "Brown-grey kind of finch" , "Bird in the finch family" , "Type of finch" , "Songster" .)

I've seen this clue in The Times and The Sunday Times.

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