Follows a daughter taking part in demonstrations (7)
I believe the answer is:
shadows
'follows' is the definition.
(shadowing is a kind of following)
'a daughter taking part in demonstrations' is the wordplay.
'a daughter' becomes 'ad' (I've seen this in other clues).
'taking part in' means one lot of letters goes inside another.
'demonstrations' becomes 'shows' (show is a kind of demonstration).
'ad' placed within 'shows' is 'SHADOWS'.
(Other definitions for shadows that I've seen before include "Dark things" , "tracks" , "Dogs" , "1960s band" , "They're cast by blocking the sun" .)