He'll shortly go down with one in capital (8)
I believe the answer is:
helsinki
'capital' is the definition.
(capital of Finland)
'he'll shortly go down with one' is the wordplay.
'shortly' means to remove the last letter.
'go down' becomes 'sink' (synonyms).
'with' is a charade indicator (letters next to each other).
'one' becomes 'I' (Roman numeral).
'hell' with its last letter removed is 'hel'.
'hel'+'sink'+'i'='HELSINKI'
'in' acts as a link.
(Other definitions for helsinki that I've seen before include "Finnish capital" , "Liken his strange city to one in Finland" , "1952 Olympic Games venue" , "Nordic capital" , "Foreign city" .)