Old-fashioned person repeating the same thing again (4)
I believe the answer is:
dodo
'old-fashioned person' is the definition.
(dodo can informally mean an old-fashioned person)
'repeating the same thing again' is the wordplay.
'repeating' shows that letters should be duplicated.
'the same thing again' becomes 'do' (do can be short for 'ditto').
'do' doubled is 'DODO'.
(Other definitions for dodo that I've seen before include "Two rooks - one was unable to fly" , "Native of Mauritius" , "one very dead!" , "One deeply reactionary" , "Proverbially dead bird" .)