With an All India Rank (AIR) of 38095 and OBC rank of 7627, it is very difficult to get a seat in any of the NLUs, even under the Tamil Nadu government school quota. Most NLUs close their OBC seats at a much lower rank. Also, the government school quota is not accepted by all NLUs.

You can still attend all rounds of CLAT counselling and keep checking for any vacancy or special rounds, but chances are very low with this rank. It is better to also look for other good law colleges as a backup.