Hard sign pointing way in school (6)

I believe the answer is:

harrow

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

'hard sign' is the wordplay.
'hard' becomes 'h' (abbreviation used in pencil classifications).
'sign' becomes 'arrow' (arrow is a kind of sign).
'h'+'arrow'='HARROW'

'pointing way in' is the link.
This may not be right. Some or all of it may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for harrow that I've seen before include "Distress greatly - public school" , "Spiked frame for breaking and levelling soil" , "Soil-breaking implement" , "worry" , "A school; agricultural implement" .)

I've seen this clue in The Times.

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