Protest by student is hard to crush (8)
I believe the answer is:
demolish
'to crush' is the definition.
(demolishing is a kind of crushing)
'protest by student is hard' is the wordplay.
'protest' becomes 'demo' (demonstration).
'by' is a charade indicator (letters next to each other).
'student' becomes 'l' (as in L-plates for learner drivers).
'hard' becomes 'h' (abbreviation used in pencil classifications).
'demo'+'l'+'is'+'h'='DEMOLISH'
(Other definitions for demolish that I've seen before include "Knock down, say a building" , "Knock or tear down" , "Eat up" , "Pull or tear down" , "Break down" .)