Bethesda didn't put a specific date on when the closed beta would kick off, but you can sign up for the Quake Champions beta right now.
The arena shooter, which promises classic Quake-style gameplay despite the introduction of classes, is due out on PC later this year. Id's accepting signups for the closed beta right now through their website, and if you have multiple email accounts you can happily refresh the page every time while selecting multiple countries (because, y'know, it's Quake).
Id noted that they'll be showcasing the first map, Blood Covenant, later this week. The video description added that more videos and details will be posted later in the week too, and if anything particularly notable appears from that we'll let you know. Until then, enjoy a very short taste of where id thinks arena shooters should be headed in 2017.