I just saw this from GameXplain that it was just announced that there is going to be an upcoming Nintendo Direct focus on E3 2021 at June 15th. This is going to be broadcast at 9 AM PT / 12 PM EST and it's going to be around 40 minutes long + Treehouse Live Event as well.
Edit from June 3rd: I'm going to post the link of the Nintendo Direct E3 2021 Stream when it's time, be sure to check it at June 15th at 9 AM PT.
Edit from Jun 14th: Nintendo just pulled up the official Nintendo Direct E3 2021 Live Stream up for tomorrow morning. Be sure to mark your watch schedule to make sure that you don't miss out on watching the Direct.