Regret getting agent to hospital department (6)
I believe the answer is:
repent
'regret' is the definition.
(I know that regret can be written as repent)
'agent to hospital department' is the wordplay.
'agent' becomes 'rep' (short for representative).
'to hospital department' becomes 'ENT' (abbreviation for Ear, Nose and Throat department).
'rep'+'ent'='REPENT'
'getting' is the link.
(Other definitions for repent that I've seen before include "Be sorry for - . . . . . . ye sinners" , "Be ashamed" , "lying on the ground" , "Feel sincere regret" , "Feel remorse for" .)