Some states are accepting NTSE registration form in online mode while some are accepting offline through schools. Kindly clarify your query to know if you can apply online or not. You can also visit the link given above to know application mode for your state.
Generally the ntse exam by ncert is carried on in offline mode every year and the fee payment for the application offline.But this year due to the current situation The application form for 2021 ntse will be made available in online mode.The application fee has to be deposited with the form itself.So the answer is yes you can apply for ntse exam 2021 online and the form also you will get in their official site.
Hope this helps!!