Shocked no one has posted this yet. According to an interview with Kotaku at PAX, the HD remake is about 80% done. The game is said also to be out by August of next year, but no exact date was given. Hajime Tabata says Square-Enix wants to wait for "the PS4 and Xbox One install base to grow in Japan as well...", so sounds as if the company is taking their time entering next-gen by allowing it to gain traction in its home country first. This also likely has to do with the delays for Final Fantasy XV as well. Although, Tabata didn't have much to say about next main instalment other than it's currently top priority for the company. New footage was also shared at PAX, but has yet to be released publicly. It's been receiving positive feeback from various gaming outlets like IGN, however.
Kotaku
IGN's Preview of Type-0 HD
Kotaku
IGN's Preview of Type-0 HD