A long time after Dorothy shows senility (6)
I believe the answer is:
dotage
'senility' is the definition.
(I know that senility can be written as dotage)
'a long time after dorothy' is the wordplay.
'a long time' becomes 'age' (an age is a period of time).
'after' says to put letters next to each other.
'dorothy' becomes 'dot' (nickname for someone called Dorothy).
'age' put after 'dot' is 'DOTAGE'.
'shows' is the link.
(Other definitions for dotage that I've seen before include "Old and weak time of life" , "Later life, when old and weak" , "Senile years" , "Old age, senility" , "when any activity may become difficult?" .)