Competitive runner from Australia mostly terrible (7)
'competitive' is the definition.
(emulous can mean showing rivalry)
'runner from australia mostly terrible' is the wordplay.
'runner from australia' becomes 'emu' (Australian animal famous for running).
'mostly' means to remove the last letter.
'terrible' becomes 'lousy'.
'lousy' with its last letter taken away is 'lous'.
(Other definitions for emulous that I've seen before include "Seeking to imitate", "Eager to equal another's deeds", "competition", "Feeling rivalry".)