Island city capital with mounting deprivation (8)
I believe the answer is:
limassol
'island city' is the definition.
(city in Cyprus)
'capital with mounting deprivation' is the wordplay.
'capital' becomes 'lima' (Lima is an example**).
'with' says to put letters next to each other.
'mounting' says the letters should be written backwards (going up in a down clue).
'deprivation' becomes 'loss' ('loss' can be a synonym of 'deprivation').
'loss' written backwards gives 'ssol'.
'lima'+'ssol'='LIMASSOL'
(Other definitions for limassol that I've seen before include "City on Cyprus" , "Port in southern Cyprus" , "found in Cyprus" , "Oil slams (anag) - Cypriot port" .)