File on hospital department is rigorous (9)
I believe the answer is:
stringent
'rigorous' is the definition.
(synonyms)
'file on hospital department' is the wordplay.
'file' becomes 'string' (file can mean a string or row).
'on' says to put letters next to each other.
'hospital department' becomes 'ENT' (abbreviation for Ear, Nose and Throat department).
'string'+'ent'='STRINGENT'
'is' is the link.
(Other definitions for stringent that I've seen before include "Demanding, inflexible" , "Tight" , "binding" , "(Rule) allowing no discretion" , "Severe, rigorous, attention to rules say" .)