One late to classes nuts must attend having crossed river (6,7)

I believe the answer is:

mature student

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'one late to classes' is the definition.
I don't know anything about this answer so I cannot judge whether it can be defined by this definition.

'nuts must attend having crossed river' is the wordplay.
'nuts' is an anagram indicator (nuts can mean crazy).
'having crossed' indicates putting letters inside.
'river' becomes 'Ure' (river in Yorkshire).
'must'+'attend'='mustattend'
'mustattend' is an anagram of 'matstudent'.
'matstudent' placed around 'ure' is 'MATURE STUDENT'.

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(Other definitions for mature student that I've seen before include "Adult scholar" , "One coming late to higher education" .)

I've seen this clue in The Times.

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