One not keeping company in sick bay (9)

I believe the answer is:

infirmary

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'sick bay' is the definition.
(I've seen this in another clue)

'one not keeping company in' is the wordplay.
'one' becomes 'i' (Roman numeral).
'not' becomes 'nary' (I've seen this in another clue).
'keeping' indicates putting letters inside (some letters kept inside).
'company in' becomes 'firm' (firm can mean a company or business. I am not sure about the 'in' bit.).
'nary' enclosing 'firm' is 'nfirmary'.
'i'+'nfirmary'='INFIRMARY'

Can you help me to learn more?

(Another definition for infirmary that I've seen is " Hospital".)

I've seen this clue in The Times.

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