I have a black belt in Taekwondo that I received at 18 years old. I'm now in my 50's. And I recently thought about getting back into it just because I want to improve my physical conditioning. I miss my youthful Taekwondo body and leg flexibility. I want some of that back. Haha.
But as for my rank, the only way I'm keeping my black belt is if the teacher allows it and the forms I learned are the same as the ones they're doing. But if either of those aren't true, then I would insist that I wear a white belt again. I prefer that, because then I have a chance to go through the foundational stuff again and build my way back up.
Throughout the years, I've received many belts in many martial arts. Each one, I had to start with a white belt. I always keep a white belt in my closet just in case. And honestly, it's a sheer joy putting on a white belt again. It means you're starting something. There's nothing but potential ahead. I can't think of anything more positive than that.
Black belts in karate are expected to teach lower ranks, too. If you're really fuzzy on all of what you learned a long time ago, then you're not ready to teach. You'll need to have a conversation with the head instructor of the school to make sure you're not put in that position. It might be a while before you're able to do things that the other black belts are doing.
Karate styles are all different. They have different forms they practice. They do different self-defense drills and one-steps. They have different ways of kicking and generating power. Everything you learned in your karate school earlier in life may end up being completely different in your new school.
So, until you come up to speed at the new school, you'll be in a bad position as a black belt. It's going to feel almost wrong. Lower ranking students will want you to answer questions, and you just won't know if your answers are "correct" at that school. You'll answer, but then you may learn you were wrong and taught the wrong thing by mistake. That's a bad feeling to have.
For the first year or so, you're going to be relentlessly corrected. Because, what you learned in the past is not only sloppy now but may also be wrong in the new school. The way you did things before maybe won't be the way things are done now in the new school. So you're going to go through a process of changing what you used to do habitually. Changing habits is hard to do. And that's going to be irritating for a while. It's going to force you to use your brain a lot more, which is actually useful for someone who's getting up in age and needs the mental workout as much as a physical one.
I always saw these differences as something to be excited about, personally. They show a different aspect on something you thought you knew. So my point is to keep an open mind, and when you're told to do something differently, it should make you very interested. This is something that will give you deeper insight into things.
My main advice is to talk with the head instructor for a while before joining up. See what they do. See if your stuff will need much correction. And tell the instructor you don't care about rank. You achieved black belt a long time ago, but that was a different you back then. You've forgotten a lot. Your body is much weaker. You're fine with wearing a white belt or any other belt so long as it's something the instructor says you should do. So leave it up to your instructor.
And then have a blast! Reconnect with your body and feel young again. Just go into it with an open mind, know what you want out of it, and keep to your own path.
Hope that helps!