Any other renowned law college still open for application for integrated law..
hello aspirant,
most of the top law exams will be held on last of may or first week of july. however there are few colleges where application process still going on,
Lovely Professional University National Eligibility and Scholarship Test (LPU NEST)
Law School Admission Test for India (LSAT India)
Bharati Vidyapeeth Deemed University Common Entrance Test (BVP CET)
Indian Law Institute Common Admission Test (ILI CAT)
Panjab University BA LLB Entrance Test (PU BA LLB Entrance)
you may also check the below links to know about more details
Yes Bharti Vidyapeeth University in Pune they are still accepting registrations for there CET exam which will be in the month of June. It's good institution you can apply for it.
Best of luck.