From the official Twitter account of the anime Kaguya-sama: Love is War, an adaptation of Aka Akasaka's manga, it has been announced that the series will have a third season and an OVA. In addition, the same Twitter account published a first promotional video.
【緊急告知】
— アニメ「かぐや様は告らせたい」公式 (@anime_kaguya) October 25, 2020
恋愛頭脳戦。それは、お互いの尊厳をかけた男女の戦いー。
この物語は、まだまだ始まったばかりなのである……。
TVアニメ「かぐや様は告らせたい」新作アニメーション製作決定#かぐや様 pic.twitter.com/KaW7o5xjPB
The OVA will launch in 2021.
The second season of the anime premiered on April 11 this year and was directed by Mamoru Hatakeyama under the animation studio A-1 Pictures. Yasuhiro Nakanishi wrote the script, Yuuko Yahiro designed the characters and Kei Haneoka composed the music.
Source: Anime Twitter account