Fast mover, iconic figure: 'Don't like being rejected!' (7)
I believe the answer is:
'fast mover' is the definition.
(cheetahs move fast)
'iconic figure don't like being rejected' is the wordplay.
'iconic figure' becomes 'Che' (iconic revolutionary Che Guevara).
'don't like' becomes 'hate' (if you hate someone you don't like them).
'being rejected' shows that the letters should be reversed in order.
'hate' back-to-front is 'etah'.
(Other definitions for cheetah that I've seen before include "Beast" , "Swift predator" , "Fast cat - the ache (anag)" , "Very fast mammal" , "Swift, spotted feline" .)