Crossword Genius

I must go in club that offers inducement (4)

Ross

I believe the answer is:

bait

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This clue could be a double definition.

'i must go in club that' is the first definition.
Although both the answer and definition are singular nouns, I don't understand how one could define the other.

'inducement' is the second definition.
(thesaurus)

'offers' is the link.

Can you help me to learn more?

(Other definitions for bait that I've seen before include "Fishing lure" , "Lure; tease" , "Worms, for example" , "Food used as lure" , "N in radio comms" .)

I've seen this clue in The Times.
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