In essence, analysts accept argument for school (6)

I believe the answer is:

lyceum

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'for school' is the definition.
(lyceum is a kind of school)

I can't explain the remainder of the clue.

(Other definitions for lyceum that I've seen before include "hall" , "School of thought" , "Garden where Aristotle taught philosophy - London theatre" , "Aristotle's teaching place" , "Aristotle's garden" .)

I've seen this clue in The Irish Times.

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