Operation cancelled with doctor beginning to fall asleep (4,3)
I believe the answer is:
drop off
'to fall asleep' is the definition.
('drop off' can be a synonym of 'fall asleep')
'operation cancelled with doctor' is the wordplay.
'operation' becomes 'op'.
'cancelled' becomes 'off' (similar in meaning).
'with' says to put letters next to each other.
'doctor' becomes 'dr' (synonyms).
'op'+'off'='opoff'
'opoff' after 'dr' is 'DROP-OFF'.
'beginning' is the link.
I am not very happy about this link. It may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for drop off that I've seen before include "Fall asleep" , "Fall < or crash" , "delivery of goods" , "Decline, decrease" .)