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On which to play casually, visiting home and part of hospital? (10)

Ross

I believe the answer is:

instrument

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

'on which to' is the definition.
I can't tell whether this definition defines the answer.

'play casually visiting home and part of hospital?' is the wordplay.
'play casually' becomes 'strum' (I've seen this before. I am not sure about the 'casually' bit.).
'visiting' indicates putting letters inside.
'home' becomes 'in' ('he's home' can mean 'he's in').
'and' is a charade indicator (letters next to each other).
'part of hospital?' becomes 'ent' (abbreviation for ear, nose and throat dept).
'in'+'ent'='inent'
'strum' inserted within 'inent' is 'INSTRUMENT'.

Can you help me to learn more?

(Other definitions for instrument that I've seen before include "legal document" , "Joanna, perhaps" , "power" , "Word puzzle" , "Means of precision work (or music-making)" .)

I've seen this clue in The Times.
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