The expression “to turn a new leaf” means to amend one’s conduct; begin a new life; go straight; reform.
The leaf that one turns is not that of a tree, but that of a book, a book of lessons or of precepts, the book on which our sins of omission and commission are recorded.
And we have been doing that, or at least using that expression for something over four hundred years.
Though not the earliest example, we find the expression in Raphael Holinshed’s Chronicles of England, Scotlande, and Irelande (1577), “He must tume the leafe, and take out a new lesson, by changing his former trade of liuing into better.”