Should I add my current supervisor as the coauthor of my paper if I am going to transfer to a new university? I am transferring to a new university. And I found a new supervisor at another university. I have told this to my current advisor. But I am still staying at the current lab as the transfer procedure would take like two or three months.
During the two months, I have been collaborating with my new supervisor on the paper and using his experimental facilities remotely. The paper is now almost finished and then we are going to publish. I will consult with my current and future supervisor. But before that, I want to ask if there is a regulation about this.
Everyone who makes a sufficient contribution to your paper for authorship should be an author on your paper (and no one else).

It doesn't matter what institution they are at nor does anything else: everyone that contributes at a level appropriate for authorship is an author.

Standards for what contribution constitutes a sufficient contribution for authorship vary by field, and your plan to consult both your new and old advisor is a good one because part of their mentorship is in helping you make decisions about what governs authorship in your field.