Grub Street journalist’s worn-out horse (4)
I believe the answer is:
hack
I believe this is a double definition.
'grub street journalist's' is the first definition.
(Grub Street, London was a centre of journalism)
'worn-out horse' is the second definition.
(Other definitions for hack that I've seen before include "Chop roughly - mediocre journalist" , "Kick on the shins" , "try to access unauthorised data" , "Tired old horse" , "Cut roughly - routine writer" .)