Hospital home with tree given by former queen (9)

I believe the answer is:

infirmary

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'hospital' is the definition.
(synonyms)

'home with tree given by former queen' is the wordplay.
'home' becomes 'in' (to be in is to be (at) home).
'with' means one lot of letters go next to another.
'tree' becomes 'fir' (fir is a kind of tree).
'given by' means one lot of letters go next to another.
'former queen' becomes 'mary' (Mary I or Mary II. I am not sure about the 'former' bit.).
'in'+'fir'+'mary'='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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