Q: Will there be, or have there been, any “late blooming” students in the school who come into their magic potential as adults, rather than as children? By the way, I loved meeting you, and hearing you speak, when you came to Anderson's in Naperville. I can hardly wait until you tour again.
JKR: Ahhh! I loved the event at Anderson’s. It was one of my favorites. That is completely true. No, is the answer. In my books, magic almost always shows itself in a person before age 11; however, there is a character who does manage in desperate circumstances to do magic quite late in life, but that is very rare in the world I am writing about.
Who was JKR referring to in “there is a character”?
Clearly, it not a student; so the most obvious guess of "Neville Longbottom" is wrong – both due to “no” answer regarding the question itself, and the fact that Neville bloomed in his 6th/7th year, well before you can legitimately term “quite late in life”.