Find out what contract you have with the other organization then talk with a lawyer.

If that contract allows what you're doing, then you're fine. But there is an excellent chance that your contract does not. In which case you need to figure out what you need to do about that.

Remember, just because you can do something doesn't mean that you're allowed to do it. And when in doubt, talk with an expert on the distinction. (That would be a lawyer.)