The main conflict would be Albus' struggle with his dad's fame and legacy which causes him to feel bad for Amos Diggory. Which ends up leading him to stealing a time-turner to try to alter time to make it so that Cedric Diggory never died at the hands of Peter Pettigrew in The Goblet of Fire. This led to Cedric joining Voldemort because he lost the Tri-Wizard Tournament. Since joining Voldemort, Cedric killed Neville Longbottom which led to Harry's death and Lord Voldemort winning the Battle of Hogwarts.
One of the themes of the book is parenthood. An example is some of the problems with Albus and his dad. Another one of the themes is legacy and caused problems for Albus to live up to his dad's legacy. One last theme would be trauma and loss. We see this when the boys explored and confronted how past events, like Cedric Diggory's death, changed Albus' view of his dad.
Harry Potter and the Cursed Child is about Harry Potters' youngest son, Albus Potter, as he struggles with his father's legacy and achievements. He forms an unlikely friendship with Scorpius Malfoy at Hogwarts, where both end up getting sorted into Slytherin. Overhearing his father refuse to help Amos Diggory, Albus and Scorpius steal a time-turner to go back and save Cedric Diggory. Their attempts to change the past created a dangerous, alternate timelines, where Voldemort never died. This revealed a bigger threat tied to Voldemort's daughter, Delphi. She managed to manipulate them to fulfill her own evil plan to resurrect her father. The plays main focus is on the problemed relationship between Harry and Albus and the Albus and Scorpius' dangerous quest to fix their mistakes. They learned that there is a reason why Harry never used the time turner to save Cedric in the first place and to live with what happened.
Work Cited
Rowling, J. K., et al. Harry Potter and the Cursed Child - Parts I & II (Special Rehearsal Edition): The Official Script Book of the Original West End Production. Little, Brown, 2016.