Best trio organised by top conductor, concerned with delivery (9)

I believe the answer is:

obstetric

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'concerned with delivery' is the definition.
I can't tell whether this defines the answer.

'best trio organised by top conductor' is the wordplay.
'organised' indicates an anagram.
'by' means one lot of letters go next to another.
'top' suggests taking the first letters.
The initial letter of 'conductor' is 'c'.
'best'+'trio'='besttrio'
'besttrio' anagrammed gives 'obstetri'.
'obstetri'+'c'='OBSTETRIC'

Can you help me to learn more?

(Other definitions for obstetric that I've seen before include "dealing with babies" , "Reproductive" , "for pregnant woman?" , "Managing birth" , "of maternity care" .)

I've seen this clue in the Sydney Morning Herald.

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