The preference of colleges/universities accepting the CLAT score are need to be submitted during the CLAT counselling. Depending on your rank you will be allotted the seats. So yeah! for CLAT the institute you have to choose will be after the examination is conducted.

For more information regarding Law colleges in India accepting the CLAT score, are provided below:

https://law.careers360.com/articles/clat-participating-institutes

I hope this helps. Wish you a great day!