Broadcasting on air with the dubious leading figure (4-4)
I believe the answer is:
anti-hero
'dubious leading figure' is the definition.
'anti hero' can be an answer for 'figure' (I have seen 'Central figure' mean 'anti hero' so perhaps 'figure' could also mean 'anti hero'). I'm not certain of the 'dubious leading' bit.
'broadcasting on air with the' is the wordplay.
'broadcasting' indicates anagramming the letters.
'with' is a charade indicator (letters next to each other).
'on'+'air'='onair'
'onair' after 'the' is 'theonair'.
'theonair' anagrammed gives 'ANTI-HERO'.
Can you help me to learn more?
(Other definitions for anti-hero that I've seen before include "Ignoble central character (of book, etc)" , "Main character in play that lacks noble qualities" , "Ignoble lead character" , "Unlovable main character" , "Weak central character of a book or drama" .)