Harassed Conservative rushed to stop introduction of higher education (8)
I believe the answer is:
hectored
'harassed' is the definition.
(I've seen this in another clue)
'conservative rushed to stop introduction of higher education' is the wordplay.
'conservative' becomes 'C' (UK political abbreviation).
'rushed' becomes 'tore' (to tear around is to rush or run fast).
'to stop' indicates putting letters inside (inserted letters plug or stop a gap).
'introduction of' suggests taking the first letters.
'education' becomes 'ed' (abbreviation - e.g. sex ed).
The first letter of 'higher' is 'h'.
'c'+'tore'='ctore'
'h'+'ed'='hed'
'ctore' going inside 'hed' is 'HECTORED'.
(Other definitions for hectored that I've seen before include "Intimidated, bullied" , "Bullied; blustered" , "Talked to bullyingly" , "Annoyed" .)