Broadcast about hospital department deputy initially being put away (4,4)
I believe the answer is:
sent down
'being put away' is the definition.
(both can mean imprisoned)
'broadcast about hospital department deputy initially' is the wordplay.
'broadcast' becomes 'sown' (broadcast can mean to sow seeds).
'about' indicates putting letters inside.
'hospital department' becomes 'ENT' (abbreviation for Ear, Nose and Throat department).
'initially' suggests taking the first letters.
The initial letter of 'deputy' is 'd'.
'ent'+'d'='entd'
'sown' enclosing 'entd' is 'SENT DOWN'.
(Other definitions for sent down that I've seen before include "Rusticated" , "imprisoned" , "Expelled from university" , "locked up" .)