Admittedly, this has already been hinted at by the closing episodes of Matt Smith's run, but I hope that Capaldi's Doctor setting off on a quest to restore Gallifrey does become the defining motive of the series. Something that enables the standard "anywhere in time and space" fare but with a hitherto unseen aspect of the Doctor's character: travelling with an objective, rather than just random exploration. Solving the "mystery" of Clara was similar in the last series, but it never seemed to become a driving motivation for the Doctor. Instead, he alternated between intense scrutiny one minute and passing curiosity the next - only once did it seem like his choice of destination was influenced by finding a way to figure her out. The Doctor is clever and well-travelled, he can probably rattle off a dozen people or places or times with technology that can help find Gallifrey which he'll want to check out. Wacky, sci-fi adventures occur along the way, of course, but with a sense of achievement by the end having taken one more step towards his goal. Though the Doctor has been given quests (after a fashion) before, this will be the first time we've seen him travelling the stars with an entirely self-interested objective and is a great chance to show new sides to the Doctor. Maybe in one episode he's given a choice between saving the "someone he barely knows but likes" character of the week or losing a seemingly sure-fire way to restore Gallifrey, and he's tempted to be selfish.
