I think that J.K.R mentions that Hermione returned to Hogwarts to complete her 7th year,but as Ron and Harry became Aurors,I am assuming that Kingsley Shacklebolt decided that they have the quality of becoming an Auror
this is from an 記事 about JK Rowling discussing what happened after the epilogue
"J.K. didn't clarify whether Harry, Ron and Hermione ever return to school to finish their seventh year, but she did say she could see Harry making an appearance every now and again to give the "odd talk" on Defense Against the Dark Arts."
Auror Interviewer: "So what is your training? What experience do あなた have?" Harry: "Well, I destroyed the Dark Lord and brought peace to the whole wizarding world which in turn saved a lot of muggles."