Hey.
The cut off for admission in any of the National Law Universities through CLAT in the previous year was a rank in the range of 1600 for the general category. Considering that your rank is  6387 you do not seem to have any chances for any of the National Law Universities.
Other than colleges with their own entrances, There are various Private Colleges that accept CLAT scores other than the National Law Universities.
Here is a list of a few of them.
Jindal Global Law School, Sonepat
Kirit P. Mehta School of Law, Mumbai
NIRMA UNIVERSITY, Ahmedabad
ICFAI Law School, HyderabadSchool of Law, GITAM University, Visakhapatnam
Alliance School of Law, Bangalore
IFIM Law College, Bangalore
LLOYD Law College,Greater Noida
Amity University, U.P.
Asian Law College, Noida
Manipal University, Jaipur

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