Single French capitalist losing heart after run on bank (8)
I believe the answer is:
riparian
'on bank' is the definition.
(term meaning on the banks of a river)
'single french capitalist losing heart after run' is the wordplay.
'single' becomes 'i' (one).
'french capitalist losing heart' becomes 'parian' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'after' says to put letters next to each other.
'run' becomes 'r' (cricket abbreviation).
'i'+'parian'='iparian'
'iparian' put after 'r' is 'RIPARIAN'.
(Other definitions for riparian that I've seen before include "along river bank" , "associated with banks" , "near a river" , "living by the river" , "Relating to a riverbank - Iran pair (anag)" .)