She started teaching at Coal Hill School sometime between "The Name of the Doctor" & "The Day of the Doctor". On screen, it was never indicated when she attended teacher's college or began her new career. Although they never made a big deal of it, there was a time jump of several years between the events of "Name of the Doctor" and "The Time of the Doctor", as Clara is said to be 24 in "The Bells of Saint John", but in "Deep Breath", which takes place immediately after "Time of the Doctor", she is said to be 27, so plenty of time to get a teaching certificate. The comic book story "Clara Oswald and the School of Death" (comic story) is the first story to directly reference Clara going to teacher's college, but it again doesn't indicate exactly when this happened. During Series 7 there is no reference to Clara attending classes while she worked as a nanny for the Maitlands.