Call about hospital department hiring (7)
I believe the answer is:
renting
'hiring' is the definition.
(I know that hiring can be written as renting)
'call about hospital department' is the wordplay.
'call' becomes 'ring' (telephone call).
'about' indicates putting letters inside.
'hospital department' becomes 'ENT' (abbreviation for Ear, Nose and Throat department).
'ring' going around 'ent' is 'RENTING'.
(Other definitions for renting that I've seen before include "Paying money for the use of" , "Leasing" .)