UPDATED: See the video of the interview, for that extra bit of Charles Dance.
An interview with Charles Dance, who plays Lannister patriarch Lord Tywin, provides the first reference we’ve seen to when the prospective season 3 will air, as well as a spoiler for those who’ve not read the novels.
Though largely focused on his appearance in SyFy’s miniseries event, Neverland, it does turn to Game of Thrones where he says the following (minus the spoiler):
Some points of interest: we know the show will air in April, not February or March, so he’s incorrect there. But the May-June date… Did he calculate that as “3 months after the premiere” or has he been told May or June? If the former, then a July shoot date may have been what he really believes (April + 3 months). That fits the start of filming for both seasons 1 and 2, although one should bear in mind that prep work can begin months earlier (I believe crew were starting preliminaries of building sets in February, before the 2nd season was even greenlit).
If, on the other hand, May or June is correct, that’s a bit earlier than the previous seasons. May, in particular, would be just a month after the premiere. If HBO holds to officially greenlighting after the first or second episode of a show, as they tend to do, that’s a very fast turnaround—fast enough that you’d have to think the production will have been told that a third season is all but certain. Which is certainly the mood among cast and crew, including some high-placed members of the production, from what we’ve been told.