Crossword Genius

One possibly hanging in the Cavern Club (3)

Ross

I believe the answer is:

bat

I'm a little stuck... Click here to teach me more about this clue!

'club' is the definition.
(as in sporting equipment)

'one possibly hanging in the cavern' is the wordplay.
I cannot quite understand how this works, but
'one' could be 'a' (a thing is one thing) and 'a' is found within the answer.
'the' could be 't' (the is pronounced as a 't' sound in some dialects) and 't' is present in the answer.
A single letter 'b' remains which might be clued in a way I don't see.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for bat that I've seen before include "Flutter (eyelids)" , "A mammal; a club" , "Nocturnal animal - racket" , "Wooden implement for cricket" , "Cricket, table-tennis and baseball implement" .)

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