Boast about Melbourne newspaper? Nonsense! (7)
I believe the answer is:
garbage
'nonsense' is the definition.
(I've seen this in another clue)
'boast about melbourne newspaper?' is the wordplay.
'boast' becomes 'brag' (synonyms).
'about' shows that the letters should be reversed in order.
'melbourne newspaper?' becomes 'age' (I can't justify this - if you can you should give a lot more credence to this answer).
'brag' back-to-front is 'garb'.
'garb'+'age'='GARBAGE'
Can you help me to learn more?
(Other definitions for garbage that I've seen before include "Waste, refuse" , "Brag about age? - that's rubbish" , "'Refuse, rubbish (7)'" , "Food waste or trash" , "A beggar? - that may be rubbish" .)