Palace supporter following city going to West Ham (8)
I believe the answer is:
alhambra
'palace' is the definition.
(palace in Spain)
'supporter following city going to west ham' is the wordplay.
'supporter' becomes 'bra' (a bra gives support to breasts).
'following' is a charade indicator (letters next to each other).
'city' becomes 'LA' (Los Angeles).
'going to west' shows that the letters should be reversed in order (letters go right to left or east to west).
'la' backwards is 'al'.
'al'+'ham'='alham'
'bra' after 'alham' is 'ALHAMBRA'.
(Other definitions for alhambra that I've seen before include "Great 14th century Moorish palace near Granada in Spain" , "Famous Moorish palace near Granada in Spain" .)