current supervisor vs. previous work
Since you already have feedback from your previous supervisor (who presumably knows the research in question much better since it was done with him) it's not critical to get feedback from your new advisor. But any feedback can be useful, especially if your new advisor is in the same area.

I would at least make your new advisor aware of the paper and ask if they want to read it, just so there won't be any surprises or perceptions that you are publishing "behind their back". Leave it up to them if they want to give you feedback or not.