Downgrade emissary on outskirts of Rome (8)
I believe the answer is:
relegate
'downgrade' is the definition.
(I've seen this before)
'emissary on outskirts of rome' is the wordplay.
'emissary' becomes 'legate' (legate is a kind of emissary).
'on' is a charade indicator (letters next to each other).
'outskirts of' means to remove the middle letters.
'rome' with its centre removed is 're'.
'legate' put after 're' is 'RELEGATE'.
(Other definitions for relegate that I've seen before include "Move to a lower division" , "Assign to a lower position" , "Put in a lower division" , "Move down to a lower grade" , "Move to a lower position" .)