Bequeathed property ending in garbage, say (6)
I believe the answer is:
estate
'bequeathed property' is the definition.
(property bequeathed in someone's will)
'ending in garbage say' is the wordplay.
'ending in' suggests the final letters.
'say' becomes 'state' (synonyms).
The last letter of 'garbage' is 'e'.
'e'+'state'='ESTATE'
(Other definitions for estate that I've seen before include "All that one owns at death" , "Rank - housing development - car" , "Property with large grounds" , "Housing area" , "Property and possessions of the deceased" .)