Rival finds dead bird first (7)
I believe the answer is:
Here is my best explanation:
'rival' is the definition.
(I've seen this before)
'dead bird first' is the subsidiary indication.
'dead' becomes 'late' ('late' can be similar in meaning to 'dead').
'bird' becomes 'emu' (emu is a kind of bird).
'first' means one lot of letters go next to another.
'late' put after 'emu' is 'emulate'.
'finds' is the link.
(Other definitions for emulate that I've seen before include "Try to match", "Rival", "Imitate - rival", "Attempt to match", "Copy -- reach equality with", "Strive to equal or better", "Follow suit", "Try to equal or excel", "Strive to equal or surpass" and "Try to equal by imitation".)