American in frightful Butlin's City (8)
I believe the answer is:
istanbul
'city' is the definition.
(Istanbul is an example)
'american in frightful butlin's' is the wordplay.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'in' indicates putting letters inside.
'frightful' indicates an anagram (a frightful spelling).
'butlins' with letters rearranged gives 'istnbul'.
'a' put into 'istnbul' is 'ISTANBUL'.
(Other definitions for istanbul that I've seen before include "Modern Byzantium" , "Eurasian city" , "Turkish port city" , "Nail bust in the Turkish city" , "City - lab units (anag)" .)