Left, in protest, is hard to break up (8)
I believe the answer is:
demolish
'break up' is the definition.
(thesaurus)
'left in protest is hard' is the wordplay.
'left' becomes 'l' (common abbreviation**).
'in' indicates putting letters inside.
'protest' becomes 'demo' (I've seen this before).
'hard' becomes 'h'.
'demo'+'is'='demois'
'l' going inside 'demois' is 'demolis'.
'demolis'+'h'='DEMOLISH'
'to' is the link.
(Other definitions for demolish that I've seen before include "Destroy completely" , "Break down" , "Eat up" , "Knock down, say a building" , "Raze to the ground" .)