Droop — though anaesthetic is rejected (3)
I believe the answer is:
sag
'droop' is the definition.
('sag' can be a synonym of 'droop')
'anaesthetic is rejected' is the wordplay.
'anaesthetic' becomes 'gas'.
'is rejected' is a reversal indicator.
'gas' back-to-front is 'SAG'.
'though' acts as a link.
(Other definitions for sag that I've seen before include "Hang down loosely" , "Lose energy" , "Decline" , "Droop in the middle - it's gas" , "fall" .)