School curtailed difficult argument (6)
I believe the answer is:
harrow
'school' is the definition.
(famous UK public school)
'curtailed difficult argument' is the wordplay.
'curtailed' means to remove the last letter.
'difficult' becomes 'hard' (synonyms).
'argument' becomes 'row' (to row is to argue).
'hard' with its last letter taken off is 'har'.
'har'+'row'='HARROW'
(Other definitions for harrow that I've seen before include "Cultivator that breaks up the soil" , "Till" , "It breaks up clods and covers seeds" , "Equipment used in ground-breaking" , "Soil-breaking implement" .)