Recalled difficulty entering top-rated British and American city areas (8)
I believe the answer is:
suburbia
'city areas' is the definition.
'recalled difficulty entering top-rated british' is the wordplay.
'recalled' is a reversal indicator.
'difficulty' becomes 'rub' (rub can mean a difficulty or problem).
'entering' means one lot of letters goes inside another.
'top-rated' becomes 'ai' (resembles Ab, informal term for excellent).
'british' becomes 'bus' (I am not sure about this - if you are sure you should believe this answer much more).
'ai'+'bus'='aibus'
'rub' put within 'aibus' is 'aibrubus'.
'aibrubus' written backwards gives 'SUBURBIA'.
'and american' is the link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
(Other definitions for suburbia that I've seen before include "Residential area away from city centre" , "Outer city regions" , "Residential district on a city's outskirts" , "Pet Shop Boys song" , "Residential districts on the outskirts of a city" .)