I want to present a piece of work done with a former PI in a conference. If I go to this conference, I use my own funding. Do I need this PI's approval to allow me to present this work in that conference? I need answers considering the 2 different scenarios: the work is either published or not published yet.
In case the work is already published, I would generally assume that everybody on this planet is allowed to talk about it, provided that the material is properly attributed. On the other hand, submitting previously published work to a conference is only possible, if the conference does not count as a publication itself (e.g., a typical computer science conference with published proceedings would be ruled out).
That would depend on a few things, including your field. What is the custom there? If the PI is, or should be, a co-author then you would need it, ethically, I think. S/he might have other plans. If the work is partly theirs, then you need it in some places legally, if I interpret other answers on this site correctly, and ethically in any case.
I'm depending on your use of the words "with a former PI" here. To me that implies they have some contribution to the work that requires acknowledgement, hence approval.
But, for political purposes and keeping good relations for the future, you should probably seek it in all cases.
In this kind of scenario, it depends on the level of privacy and contribution of the PI to the conference material.
Another case is maybe it will be more beneficial if you just try to get the approval from your formal PI (
taking the bull by the horn), which now depends on them if they approved it or not...
You are free to present it.