Variety reports that Jeff Nichols has been hired to write and direct the film, and that the plot is based on an original idea thought up by John Krasinski. Note that Krasinski directed and co-wrote both Quiet Place films so far, also co-starring in the first one.
As for Nichols, his resume includes writing/directing credits for the dramas Loving, Mud, and Midnight Special, among others.
The original Quiet Place, which came out in 2018, co-starred Emily Blunt (see: Krasinksi's real-life wife) and made over $340 million at the worldwide box office off a sub-$20 million budget. In addition to that being more than enough to get future films made, the release also set a new record for the biggest opening weekend for an original (non-adapted) horror movie by pulling in over $50 million in its first few days in theaters. It was also very well-received by critics, and got an Oscar nomination for sound editing.
As for the planned third film's story details, those currently do not exist...or at least they're not available to the public. The Hollywood Reporter writes that it will be a "spinoff connected to the events" of the first movie. The film is set to come out at some point in 2022. So, hopefully theaters will be open by then.