Can I apply for Common law admission test after having compartment/supplementary in any subject in 12th grade

no, if you have compartment/supplementary in any subject in 12th grade than you are not eligible to apply for Common law admission test.. firstly you should clear the 12th grade examination to apply for CLAT .

Eligibility:

For Under-Graduate Courses:
You should have completed Senior Secondary School/Intermediate (10+2) or its equivalent certificate from a recognized Board with not less than 45% marks in aggregate.

Participating law schools:
National Law School of India University
Nalsar University of Law
The West Bengal National University of Juridical Sciences
Dr. Ram Manohar Lohia National Law University
Chanakya National Law University
National University of Advanced Legal Studies
National University of Study and Research in Law
National Law University, Orissa
National Law University and Judicial Academy, Assam
Rajiv Gandhi National University of Law
National Law Institute University
National Law University, Jodhpur
Hidayatullah National Law University
Gujarat National Law University