Count on a northern city that's disheartened finding hope (10)
I believe the answer is:
expectancy
'hope' is the definition.
(thesaurus)
'count on a northern city that's disheartened' is the wordplay.
'count on' becomes 'expect' (to count on something is to expect it to happen).
'northern' becomes 'n' (abbreviation e.g. N. Ireland).
'that's disheartened' suggests removing the centre.
'city' with its middle removed is 'cy'.
'expect'+'a'+'n'+'cy'='EXPECTANCY'
'finding' is the link.
(Other definitions for expectancy that I've seen before include "Anticipation" , "See 21" .)