Do I need permission from my past supervisor? I am currently a postdoc in computer science. Last year I completed my PhD. I have published one research paper during my PhD with my research supervisor. I am trying to work on that paper. I mean I have got something and I think it is going to be an incremental result of the previous research paper.

Question: Do I need to get permission from my past supervisor to publish a paper that builds on our previous co-authored paper?
If your past supervisor made a significant intellectual contribution to the new paper, then he should be a coauthor.  And then, yes, you need his permission to publish the paper, because publication requires the consent of all coauthors.

If your past supervisor did not make a significant intellectual contribution to the new paper, then he should not be a coauthor.  And then no, you don't need his permission to publish the paper, because he is not a coauthor.

In short: The fact that he is your former supervisor is utterly irrelevant.  (This would also be true if he were your current supervisor.)