Rival finds dead bird first (7)
I believe the answer is:
emulate
'rival' is the definition.
(thesaurus)
'dead bird first' is the wordplay.
'dead' becomes 'late' ('late' can be similar in meaning to 'dead').
'bird' becomes 'emu' (emu is a kind of bird).
'first' says to put letters next to each other.
'late' after 'emu' is 'EMULATE'.
'finds' is the link.
(Other definitions for emulate that I've seen before include "Follow suit" , "Mimic" , "Copy - rival" , "Try to match" , "Model oneself on" .)