Hospital department -- it was first to be named (8)
I believe the answer is:
entitled
'named' is the definition.
(entitling is a kind of naming)
'hospital department it was first' is the wordplay.
'hospital department' becomes 'ENT' (abbreviation for Ear, Nose and Throat department).
'was first' becomes 'led' (to lead is to go first).
'ent'+'it'+'led'='ENTITLED'
'to be' acts as a link.
(Other definitions for entitled that I've seen before include "Named, called" , "As a book is in front" , "with style" , "Having a right (to something)" , "Given right - named" .)