American's rotten luck with southern city (8)
I believe the answer is:
auckland
'city' is the definition.
(I know that Auckland is a city)
'american's rotten luck with' is the wordplay.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'rotten' is an anagram indicator.
'with' becomes 'and'.
'luck' is an anagram of 'uckl'.
'a'+'uckl'+'and'='AUCKLAND'
'southern' acts as a link.
I am not very happy about this link. It may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for auckland that I've seen before include "Seaport on North Island in New Zealand" , "Principal port of New Zealand" , "NZ city" , "Largest city on New Zealand's North Island" , "Province and largest city of New Zealand" .)