School breaks up (6)

I believe the answer is:

harrow

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'school' is the definition.
(famous UK public school)

I cannot understand how the rest of the clue works.

(Other definitions for harrow that I've seen before include "Plough, school" , "English public school - farm implement" , "Agricultural frame for breaking up soil" , "Cultivator that breaks up the soil" , "Soil-breaker; school" .)

I've seen this clue in the Evening Standard.

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