Eight are bothered with inheritance (8)
I believe the answer is:
heritage
'inheritance' is the definition.
('heritage' can be a synonym of 'inheritance')
'eight are bothered' is the wordplay.
'bothered' indicates an anagram.
'eight'+'are'='eightare'
'eightare' anagrammed gives 'HERITAGE'.
'with' acts as a link.
(Other definitions for heritage that I've seen before include "Ancestry" , "That which is passed down from ancestors" , "Objects and cultural traditions passed down" , "NT's domain" , "Treasured historic items" .)