Underground part of a hospital (3)

I believe the answer is:

pit

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'underground part' is the definition.
'pit' can be an answer for 'part' (I have seen 'part of theatre' mean 'pit' so perhaps 'part' could also mean 'pit'). I am unsure of the 'underground' bit.

'of a hospital' is the wordplay.
'of' indicates the answer is hidden within the clue.
'PIT' is hidden within 'hospital'.

Can you help me to learn more?

(Other definitions for pit that I've seen before include "Cherry stone" , "Large deep hole in the ground" , "A hole as for coal" , "Tip into crater" , "Match (one's wits); mine" .)

I've seen this clue in the Evening Standard.

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