The BBC is keeping mum about when exactly the new series of Sherlock will air, though I think my estimate is logical. To make up for their silence, they've released this image from the new series, which others are saying is a still from the premiere episode, The Empty Hearse, though to me it looks far more like a staged publicity shot that a depiction of an event from the episode.
Now, if you'll excuse me as I move from reporting into full-on supposition mode, I have a theory as to when we'll get an official announcement about the air date. Despite the internet being able to spread the news around faster than an STD on a college campus, the BBC would primarily want an opportunity to broadcast the news when they would have the maximum potential audience. A time when whole families might conceivably be sitting down to watch programming. I therefore predict that the air date, along with possibly a new trailer for series 3, will air following the Day of the Doctor.
Mark my words, and if I'm wrong, may that not teach me not to make wild guesses.
Via Collider.