Unlimited happy medicine for chosen person (11)

I believe the answer is:

appointment

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'chosen person' is the definition.
'appointment' can be an answer for 'person' (appointment is a kind of person). I am unsure of the 'chosen' bit.

'unlimited happy medicine' is the wordplay.
'unlimited' says to take the centre (remove the limits/outer letters).
'medicine' becomes 'ointment' (ointment is a kind of medicine).
The middle letters of 'happy' are 'app'.
'app'+'ointment'='APPOINTMENT'

'for' acts as a link.

Can you help me to learn more?

(Other definitions for appointment that I've seen before include "German city" , "Meeting" , "Post" , "Engagement" , "Date" .)

I've seen this clue in The Times.

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