Where was Hermione's time turner after the Prisoner of Azkaban?
In Harry Potter, Hermione's Time turner saves the day in the Prisoner of Azkaban.
But then we don't see it in the rest of the series.
Where did it go?
She returned it.
Hermione Granger got one from Professor McGonagall to attend more classes in her third year than time would allow. Since McGonagall made her swear to not tell anyone about it, she did not mention it to Harry Potter or Ron Weasley until the end of the school year, when she and Harry used it to travel back in time and save Sirius Black and Buckbeak from certain death.
They took special permission from the Ministry of Magic to allow Hermione to use one, but her academic record ensured that permission was given.
Hermione found her third year stressful with the extra class load, and therefore dropped Divination and Muggle Studies. So, she was back to normal schedule and she returned her Time-Turner.