Start to regain consciousness, despite anaesthesiologist's conclusions (5)
I believe the answer is:
onset
'start' is the definition.
(both can mean the beginning of something)
'to regain consciousness despite anaesthesiologist's conclusions' is the wordplay.
'conclusions' indicates one should take the final letters (I've seen 'conclusion' mean this).
The final letters of 'to regain consciousness despite anaesthesiologist' are 'ONSET'.
(Other definitions for onset that I've seen before include "Start, beginning" , "Attack using stone" , "Advent" , "Assault; start" , "Beginning (of something often unpleasant)" .)