During the Kadokawa Light Novel Expo 2021 , it was revealed that the 4th season of the Date A Live anime will arrive in October of this year. According to the official website , it will be directed by Jun Nakagawa (Date A Bullet, High School Fleet).
Check out the promotional image released:

Synopsis:
Shido Itsuka meets a beautiful young woman named "Tohka," the only problem being that she was the cause of a cataclysm that destroyed a large part of humanity 30 years ago.
Thus, the novel by authors Koushi Tachibana and Tsunako was published between March 2011 and March 2020, totaling 22 volumes. An anime adaptation with 12 episodes was animated by AIC Plus in April 2013, and its second season with 10 episodes by JC Staff , which premiered in April 2014.
Finally, due to the immense success of Date A Live , a third season of 12 episodes arrived in January 2019.
