Yes, CBSE private student can apply for CLAT entrance Exam as there is no any such kind of restriction. As per the eligibility you should have minimum 45% as a General category & 40% as a Reserved category in class 12th board.

 You can check the further exam eligibility with the given below link.

https://law.careers360.com/articles/clat-eligibility-criteria

Good Luck!

Yes cbse student can apply, they need to qualify 12th board examination under 10+2 school system with at least 45 per cent marks in aggregate of the subjects appeared in the 12th board examination. Moreover, those belonging to SC/ST need to score at least 40 per cent marks in the aggregate of subjects