Follow a daughter during demonstration (6)
I believe the answer is:
shadow
'follow' is the definition.
(shadowing is a kind of following)
'a daughter during demonstration' is the wordplay.
'a daughter' becomes 'ad' (I've seen this in other clues).
'during' means one lot of letters goes inside another.
'demonstration' becomes 'show' (show is a kind of demonstration).
'ad' inserted into 'show' is 'SHADOW'.
(Other definitions for shadow that I've seen before include "Image caused by obscuring of light" , "Follow; partial darkness" , "Trace - dog" , "Secret follower" , "It's cast when light is blocked" .)