The application for HSEE Exam 2021 , has not started yet. But it is expected to start soon. IIT Madras will provide the online facility for HSEE 2021 registration to candidates from the third week of December 2020 at hsee.iitm.ac.in. So, you can check this link for more updates. You can also refer to the link given below, to get more info.
Hope it helps.