Inherited dilapidated cinema on the borders of Tokyo (4,4)

'inherited' is the definition.
('come into' can be a synonym of 'inherit')

'dilapidated cinema on the borders of tokyo' is the wordplay.
'dilapidated' indicates anagramming the letters.
'on' says to put letters next to each other.
'the borders of' says to hollow out the word (remove centre letters).
'tokyo' with its centre removed is 'to'.
'cinema' anagrammed gives 'camein'.
'camein'+'to'='CAME INTO'