Bird delayed rival successfully (7)
I believe the answer is:
emulate
'rival successfully' is the definition.
(I've seen this in another clue)
'bird delayed' is the wordplay.
'bird' becomes 'emu' (emu is a type of bird).
'delayed' becomes 'late' (running late).
'emu'+'late'='EMULATE'
(Other definitions for emulate that I've seen before include "Try to do as well as another" , "Copy - rival" , "Try to be equal or better than" , "Imitate - rival" , "ambitious veteran" .)