There are 4 scheduled OVAs to be released, with 2 of them being already aired. The 3rd one will be released on May 2nd and it will take place at a hot spring right after the end of the 2nd season.
The 4th and final one is also taking place right after the end of the 2nd season but, compared to the 3rd one, it has canon material. This OVA is about the Autumn Leaf Viewing event (manga chapters 117-119), with the 2nd season ending with chapter 116.
Autumn Leaf Viewing event
The Autumn Leaf Viewing event is a campus wide event at Tōtsuki Culinary Academy that takes place right after the Stagiaire event.
This event allows the first-year high school students currently in the academy to meet other students in other generations.
For those who participated in the main tournament of the Tōtsuki Autumn Election in that respective year, they spend their time during the event meeting the current Elite Ten Council.