Curtailed complex argument in school (6)
I believe the answer is:
harrow
'school' is the definition.
(famous UK public school)
'curtailed complex argument' is the wordplay.
'curtailed' means to remove the last letter.
'complex' becomes 'hard' ('hard' is associated in meaning with 'complex').
'argument' becomes 'row' (I've seen this before).
'hard' with its last letter removed is 'har'.
'har'+'row'='HARROW'
'in' is the link.
(Other definitions for harrow that I've seen before include "Soil-breaker; school" , "English public school - farm implement" , "Cultivator that breaks up the soil" , "Till" , "Plough, school" .)