Literary rascal perhaps cracked up on the air (8)
I believe the answer is:
antihero
'literary rascal perhaps cracked' is the definition.
I can't tell whether this defines the answer.
'up on the air' is the wordplay.
'up' indicates anagramming the letters (letters get chucked up).
'on'+'the'+'air'='ontheair'
'ontheair' with letters rearranged gives 'ANTIHERO'.
Can you help me to learn more?
(Other definitions for antihero that I've seen before include "ignoble character" , "Principal character without virtue" , "Less than admirable character" , "Protagonist without admirable qualities" , "principal character lacking noble qualities" .)