Rejected rubbish had to be reduced (7)
I believe the answer is:
refused
'rejected' is the definition.
('refuse' can be a synonym of 'reject')
'rubbish had to be reduced' is the wordplay.
I cannot really understand how this works, but
'rubbish' could be 'refuse' (both can mean waste material) and 'refuse' is found in the answer.
'had' could be 'd' (in contractions e.g. 'I'd', 'you'd' etc) and 'd' is located in the answer.
This accounts for all the letters.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for refused that I've seen before include "Declined, rejected" , "Was unwilling to accept" , "Said no (7)" , "turned down appeal" , "Not accepted" .)