County councillor accepting nothing new disheartened everybody (8)
I believe the answer is:
cornwall
'county' is the definition.
'councillor accepting nothing new disheartened everybody' is the wordplay.
'councillor' becomes 'cr' (abbreviation).
'accepting' means one lot of letters goes inside another (inserted letters are accepted).
'nothing' becomes 'O' (O resembles 0).
'disheartened' says to hollow out the word (remove centre letters) (the middle or heart is removed).
'everybody' becomes 'all' (all people).
'new' with its centre removed is 'nw'.
'cr' going around 'o' is 'cor'.
'cor'+'nw'+'all'='CORNWALL'
(Other definitions for cornwall that I've seen before include "Land" , "County in southwestern England" , "Southwestern English county" , "Southern English county" , "County in SW England" .)