Go into medical department, with hesitation (5)
I believe the answer is:
enter
'go into' is the definition.
('enter' can be a synonym of 'go into')
'medical department with hesitation' is the wordplay.
'medical department' becomes 'ent'.
'with hesitation' becomes 'er' (I've seen this in other clues).
'ent'+'er'='ENTER'
(Other definitions for enter that I've seen before include "Record - stage direction - come in" , "Come/go in" , "Go in - set down" , "Register formally as a participant" , "Come in - register" .)