A long time after dropping cage (7)
I believe the answer is:
dungeon
'cage' is the definition.
'a long time after dropping' is the wordplay.
'a long time' becomes 'eon' (eon is a kind of long time).
'after' is a charade indicator (letters next to each other).
'dropping' becomes 'dung'.
'eon' put after 'dung' is 'DUNGEON'.
(Other definitions for dungeon that I've seen before include "Underground prison-cell" , "part of prison" , "Dark prison cell" , "Keep" , "Prison cell, often underground" .)