Anaesthetised by a French doctor injecting drug (5)
I believe the answer is:
under
'anaesthetised' is the definition.
(I've seen this before)
'a french doctor injecting drug' is the wordplay.
'a french' becomes 'un' ('a' in French).
'doctor' becomes 'dr' ('Dr' can be a synonym of 'doctor').
'injecting' indicates putting letters inside.
'drug' becomes 'e' (e is another name for ecstasy).
'dr' going around 'e' is 'der'.
'un'+'der'='UNDER'
'by' is the link.
(Other definitions for under that I've seen before include "Subject to the authority of" , "One prepared to take over from leading actor" , "Subordinate to; planted with" , "In a state of unconsciousness" , "Being short" .)