Go into hospital department with hesitation (5)
I believe the answer is:
enter
'go into' is the definition.
(enter can mean to go into a place)
'hospital department with hesitation' is the wordplay.
'hospital department' becomes 'ENT' (abbreviation for Ear, Nose and Throat department).
'with' means one lot of letters go next to another.
'hesitation' becomes 'er' (sound used when hesitating).
'ent'+'er'='ENTER'
(Other definitions for enter that I've seen before include "Register formally as a participant" , "Enrol" , "A key on the right" , "Go/come in" , "Introduce" .)