Is it OK to submit a paper without asking your former supervisor?
You should never submit a paper without the active consent of the co-authors.  If your advisor is a co-author (and they probably will be for work based on your Masters thesis), then you definitely must have their consent to submit.  You can do most of the writing yourself, if you want, since you probably have more time to devote to this than your advisor, but you should talk with your advisor about your intent early in the process and must determine authorship.

Addressing the follow-on question in your edit: new research conducted independently from any work done during your Masters, however, need not have your advisor as a co-author.