For a bonus, there's no such thing! (5)

I believe the answer is:

claim

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'thing' is the definition.
The definition and answer can be both acts as well as being singular nouns.
Maybe you can see a link between them that I don't see?

I cannot understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for claim that I've seen before include "Allege" , "Cause the loss of (a life)" , "Assertion; demand" , "Assert; request" , "title" .)

I've seen this clue in the Evening Standard.

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