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Cunning
tabloid,
perhaps,
that
can
catch
pests
(8)
Cunning tabloid, perhaps, that can catch pests (8)
hints
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checks
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hints
The definition is at the end of the clue.
How the clue works
That can catch pests is your definition — flypaper being the classic fly-trapping sheet. Then the wordplay builds it up: FLY gives you "cunning" (as in a fly old fox), and PAPER is your tabloid, perhaps, so put them together and there it is.