Theatre is in medicine-management department (6)
I believe the answer is:
cinema
'theatre' is the definition.
(I know that cinema is a type of theatre)
'in medicine-management department' is the wordplay.
'in' indicates the answer is hidden within the clue.
'CINEMA' is hidden in the letters of 'medicine management department'.
'is' is the link.
(Other definitions for cinema that I've seen before include "(Building for) the movies" , "Place of entertainment" , "Film industry" , "Filmdom" , "Movie-house" .)