Not only are you afraid of the board exams, the CLAT Consortium is too.
According to the official notification here, the exam has been rescheduled to happen on 13th of June.
The notification says:
The Executive Committee of the Consortium of National Law Universities met on 6th January, 2021 to consider rescheduling the date of the CLAT 2021 exam due to clashes with the CBSE Board examination schedule announced last week.
The date for CLAT 2021 has been rescheduled to Sunday, the 13th of June, 2021 from 2.00 PM to 4.00 PM.
The UG and LL.M. exams shall be conducted on this date.