Nowadays, there are two types of LLB courses available. One is the five year integrated LLB Course which is purused right after your 12th grade. The other is 3 year LLB program which is purusued after doing a graduation degree. Therefore, once your B.E. course is finished, you can apply for 3 year law courses. Some of the colleges which offer three-year law courses are Faculty of Law (Delhi University), Banaras Hindu University, Aligragh Muslim Univeristy etc.
However, CLAT is solely for the purpose of admission in National Law Univerisities to be purusued after 12th Standard.
You can apply not at all problem actually for this entrance exam is 12th class with minimum 45% is enough so don't worry about this issue
You can apply for the clat for sure
Best of luck