According to a message on the main menu of the Battlefield 1 Closed Alpha, that particular test will end on July 18 for PlayStation 4, Xbox One, and PC, with the servers going offline at 1am PT/4am ET.
The message also states:

We hope you’ve been enjoying war on an epic scale with the Battlefield 1 Closed Alpha. We appreciate you taking time to play, and for providing feedback on the gameplay. Your feedback on the Weapon, Class, and Vehicle balancing is extremely helpful as we look to improve the experience.

With just four days to go in the Alpha, DICE wrote on Twitter, “We?re not currently accepting new players into the Closed Alpha.”
Earlier today, it was reported that Sebastian Moritz, Battlefield’s German Community Manager, said the open Battlefield 1 Beta would take place after gamescom 2016 in mid-August. However, according to a new translation of the interview, Moritz replied with “you said that not me” when the Twitch streamer suggested post-gamescom would be a good time-frame for the beta. Asked about the open beta on Twitter today by numerous people, DICE is still only saying that it’s happening “later this year” on PS4, Xbox One, and PC. “Once we have the dates and other details for the public Beta, we’ll share that info on our official channels,” they add.
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