Settler right behind City institution (4)
I believe the answer is:
boer
'settler' is the definition.
'right behind city institution' is the wordplay.
'right' becomes 'r' (common abbreviation).
'behind' means one lot of letters go next to another.
'city institution' becomes 'boe' (bank of england).
'r' after 'boe' is 'BOER'.
(Other definitions for boer that I've seen before include "Dutch-descended South African" , "South African such as President Kruger" , "Dutch settler in southern Africa" , "Afrikaans speaker" , "Robe worn by S African rebel" .)