Many people never run into their T outside of sessions. I've never seen my current T anywhere except in her building. However, I used to see my former T in my community at social events and I would say hello to her and maybe make small talk for a couple of minutes. She always spoke to me if I spoke to her first. Once she waved to me in a restaurant. We never spoke at length; it would have been awkward.

Many Ts don't acknowledge their clients in public because it could be awkward for the client. If you do, a brief hello and, at the most, a couple of minutes of small talk would be all that is appropriate. My T and I did have something in common, so we talked a minute or two.

I think it would be more than a coincidence if you run into your new T at events the way you did your former T, don't you?

You can ask your new T what her or his boundaries are, and if he or she will acknowledge you if you meet in public.