I agree with evaoslik. A parent couldn't say their child is “a new chapter for itself”. I don't think it would be
understood.
The problem (in English) here is with the word “chapter”, which can only
be used (as a Google search shows) in the context of books, or
in a context where we can assume that some kind of “record” or “history”
is being written or likely to be written, and very often “new chapter for
itself” is used because of the play on words (book, chapter).
In the case of a child, there's no “book” reference and we can't
assume that a “story” or “history” about the
child's temperament is being written or likely to be written. But the parent
could say “I could write a book about him/her” to describe
their child's character, behaviour, etc.