Pulls out of hospital procedure after doctor gives you bug (9)
I believe the answer is:
eavesdrop
'bug' is the definition.
(thesaurus)
'pulls out of hospital procedure' is the wordplay.
'pulls' becomes 'heaves'.
'out of' indicates named letters should be taken away.
'hospital' becomes 'h'.
'procedure' becomes 'drop' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'heaves' with 'h' taken away is 'eaves'.
'eaves'+'drop'='EAVESDROP'
'after doctor gives you' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
(Other definitions for eavesdrop that I've seen before include "Listen at windows" , "Listen secretly to a private conversation" , "Hold secret hearing" , "Deprave so to listen secretly" , "Listen in secret" .)