You can apply to get into ISI Kolkata in two ways each year. Usually, right after the GATE exam, they post an advertisement in the paper for admissions. 

After this, you can do the following:

• First, take the written test provided by the college for admission and if you crack it, you will qualify for the interview process.
• Secondly, if you have given GATE, you will be called directly for the interview if you have scored well.

But, make sure that you do well in the interview. This is the final qualifier for obtaining admission.