Generally you’ll only need a Master’s to get Tenure.
Art Schools usually don’t offer tenure, and so the Master’s isn’t always needed.
In a University setting, the Masters is recognized as the terminal degree but the nature of the program and your thesis should be related to Design and the research you’ll be publishing in order to get tenure.
(for example, sustainability isn’t strictly design but it’s taught to design students. so you could use a masters in sustainability for your University required terminal degree and teach/publish sustainability once hired on)