Extinct bird makes the party - twice! (4)
I believe the answer is:
dodo
'extinct bird' is the definition.
(I've seen this before)
'the party twice' is the wordplay.
'the party twice' means two replacements for 'party'.
'party' becomes 'do' (do is a kind of party).
'party' becomes 'do' (do is a kind of party).
'do'+'do'='DODO'
'makes' is the link.
(Other definitions for dodo that I've seen before include "One deeply reactionary" , "Old bird" , "Flightless bird, extinct since the 17th century" , "Old fogey" , "bird long dead" .)