Fellow on tree comes to grief at start of book (7,3)

I believe the answer is:

chapter one

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'start of book' is the definition.
I don't know anything about this answer so I can't tell whether it can be defined by this definition.

'fellow on tree comes to grief' is the wordplay.
'fellow' becomes 'chap' (both can mean a man).
'comes to grief' is an anagram indicator.
'on'+'tree'='ontree'
'ontree' is an anagram of 'terone'.
'chap'+'terone'='CHAPTER ONE'

'at' acts as a link.

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I've seen this clue in the Evening Standard.

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