Manage - to administer the anaesthetic to? (4,3)
I believe the answer is:
make out
'manage' is the definition.
(thesaurus)
I don't understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for make out that I've seen before include "Manage to see" , "Discern" , "Distinguish; pretend" , "Descry - succeed" , "understand" .)