Horseman in an old city going after money (7)
I believe the answer is:
centaur
'horseman' is the definition.
(half horse, half man)
'an old city going after money' is the wordplay.
'an' becomes 'a'.
'old city' becomes 'ur' (ancient city state).
'going after' is a charade indicator (letters next to each other).
'money' becomes 'cent' (eg denomination of dollars).
'a'+'ur'='aur'
'aur' put after 'cent' is 'CENTAUR'.
'in' is the link.
(Other definitions for centaur that I've seen before include "Mythical creature, half-man, half-horse" , "Mythical equine creature" , "Mythic man-horse" , "Mythological creature" , "Horsey person" .)