Nope. You can subscribe/post/comment on any community on any instance. There is one small seam though: if you're the first person to subscribe from your instance, you need to put in the full URL of the community (https://lemmy.ml/c/gaming, for example) to pull it into your instance.
After that, everybody on the same instance as you will see it when searching for communities just like it was local.
EDIT: Oh, forgot to mention: make sure the search is set to "All", not "Communities" when you do this.
Go to Communities at the top, change the filter from "Local" to "All" and search for "Gaming".
If you're the first one who wants to register to a community from this server (not the case here) it's slightly more complex.