Take up residence outside a Washington city (7)
I believe the answer is:
seattle
'washington city' is the definition.
(I've seen this before)
'take up residence outside a' is the wordplay.
'take up residence' becomes 'settle' ('settle' can be a synonym of 'take up residence').
'outside' indicates putting letters inside.
'settle' going around 'a' is 'SEATTLE'.
(Other definitions for seattle that I've seen before include "somewhere in Washington" , "US West coast port" , "Washington port" , "Sleepless in --, film" , "Place in Washington" .)