He's rich, eccentric and fourth in line for county (8)
I believe the answer is:
cheshire
'for county' is the definition.
(I've seen this before)
'he's rich eccentric and fourth in line' is the wordplay.
'eccentric' is an anagram indicator.
'and' is a charade indicator (letters next to each other).
'fourth in line' becomes 'e' (4th letter of 'line').
'hes'+'rich'='hesrich'
'hesrich' anagrammed gives 'cheshir'.
'cheshir'+'e'='CHESHIRE'
(Other definitions for cheshire that I've seen before include "Crumbly cheese from northwest England" , "English cheese or cat" , "Cat with broad smile, from English county" , "division in England" , "part of England" .)