Rival finds dead bird first (7)
I believe the answer is:
Here is my best explanation:
'rival' is the definition.
'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 "Try to do as well as, copy", "Imitate - rival", "To rival", "Ape", "Match by imitation", "ambitious veteran", "Try to equal by imitation", "Try to be like", "Strive to equal or surpass" and "Try to equal or excel".)