Successfully rival Parky's nemesis after time (7)
I believe the answer is:
emulate
'successfully rival' is the definition.
'emulate' can be an answer for 'rival' (I've seen this before). I am unsure of the 'successfully' bit.
'parky's nemesis after time' is the wordplay.
'parky's nemesis' becomes 'emu' (I've seen this before).
'after time' becomes 'late' (I've seen this in other clues).
'emu'+'late'='EMULATE'
Can you help me to learn more?
(Other definitions for emulate that I've seen before include "Mimic" , "Try to be equal or better than" , "Follow suit" , "Strive to equal or better" , "Compete" .)