Refuse to boast about one's years (7)
I believe the answer is:
'refuse' is the definition.
(I know that refuse can be written as garbage)
'boast about one's years' is the wordplay.
'boast' becomes 'brag' (brag is a kind of boast).
'about' shows that the letters should be reversed in order.
'one's years' becomes 'age'.
'brag' back-to-front is 'garb'.
'to' acts as a link.
(Other definitions for garbage that I've seen before include "Refuse - worthless talk" , "Rubbish, waste" , "Waste, refuse" , "'Refuse, rubbish (7)'" , "Litter" .)