Family’s experiences after descending on a foreign city (8)
I believe the answer is:
kinshasa
'foreign city' is the definition.
(capital of the Democratic Republic of the Congo)
'family's experiences after descending on a' is the wordplay.
'family's' becomes 'kin's' ('kin' can be a synonym of 'family').
'experiences' becomes 'has' (have can mean to experience or go through).
'after descending on' means one lot of letters go next to another (in a down clue, some letters go above others).
'kins'+'has'+'a'='KINSHASA'
(Other definitions for kinshasa that I've seen before include "Capital of Dem Rep of the Congo" , "Congolese port" , "African capital on the Congo River" , "Capital of Zaire" , "It was formerly Leopoldville" .)