Demonstration succeeded - and how! (4)
I believe the answer is:
show
'demonstration' is the definition.
(show is a kind of demonstration)
'succeeded and how' is the wordplay.
'succeeded' becomes 's' (genealogical abbreviation).
'and' says to put letters next to each other.
's'+'how'='SHOW'
(Other definitions for show that I've seen before include "Performance" , "Entertainment - guide" , "The world of entertainment" , "Labour's evidence for starting" , "Portray" .)