President to want Republican backing in East Coast city (8)
I believe the answer is:
aberdeen
'east coast city' is the definition.
(city on Scotland's east coast)
'president to want republican backing' is the wordplay.
'president' becomes 'abe' (Abraham (Abe) Lincoln).
'to want' becomes 'need' ('need' can be a synonym of 'want').
'republican' becomes 'r' (abbreviation).
'backing' shows that the letters should be reversed in order.
'need'+'r'='needr'
'needr' reversed gives 'rdeen'.
'abe'+'rdeen'='ABERDEEN'
'in' acts as a link.
(Other definitions for aberdeen that I've seen before include "Bare need to be in Scottish city, oddly" , "somewhere in Scotland" , "Scottish East coast city" , "city in Europe" , "Victorian premier" .)