"….many wizards overlook the importance of choosing the right spell but this really matters. I think it's a much-underestimated part of modern witchcraft."
-- Scorpius Malfoy (CC3.16)
After hearing what happened after the last use of the Time-Turner – and how there was a world where Lord Voldemort triumphed over Harry Potter, Delphi takes it from the boys and reveals herself as manipulative and evil. She wants to become “The Augurey” and alter time so that Voldemort will be in power (CC3.16).
At the same time or just after the previous event, likely October 2020
This event takes place in the Repaired timeline, as described in the essay "Albus Potter and the lesson in Quantum Mechanics" by Nick Moline.
Delphi says about her Augurey tattoo that "it reminds me that the future is mine to make". Initially, Albus thinks this is "cool". However, Delphi also has a vision, from the information Scorpius and Albus have told her about Cedric Diggory as a Death Eater, of what one possible future looks like. But this future is only going to happen if she can change the world to where she is "The Augurey" and Lord Voldemort prevails (CC3.16).
From the Web
Pottermore: Harry Potter and the Cursed Child
The theatre production opened in the West End of London at the Palace Theatre on 30 July 2016, with Esther Smith in the role of Delphi, Sam Clemmett as Albus Potter and Anthony Boyle as Scorpius Malfoy: Harry Potter and the Cursed Child, Parts One and Two