Hey,
CLAT or Common Law Aptitude Test is a national level entrance examination for undergraduate and postgraduate law courses in India offered by National Law Universities and other institutions.
Other than CLAT,there are several other Universities that conduct their own national level law exams like Jamia Milia Islamia,Banaras Hindu University,Aligarh Muslim University,Lovely Proffessional University etcetra.
For detailed information about the examination dates etcetra follow the link given below:
https://law.careers360.com/exams
Hope this helps.
Good luck.