Most important anaesthetic assigned to surgeries centrally (6,3)
I believe the answer is:
number one
'most important' is the definition.
(I've seen this before)
'anaesthetic assigned to surgeries centrally' is the wordplay.
'anaesthetic' becomes 'number' (i.e. something that makes things numb).
'assigned to' means one lot of letters go next to another.
'surgeries centrally' becomes 'one' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'number'+'one'='NUMBER ONE'
Can you help me to learn more?
(Other definitions for number one that I've seen before include "Cut" , "Chief - First Lieutenant - myself" , "Yours truly" , "leader" , "the most important person" .)