A department could have information that is not necessarily related to national security. I cannot give a specific example, but it could involve any government organization that has information that meets the criteria set out in the definition.
First, according to the definition, the information must actually undermine the sovereignty, security or territorial integrity of Canada. Then, we would need to see, of the 17 institutions set out in Schedule 3, which mandate relates to this type of information. If the relevance criteria is met, then the organization in question can share the information. An institution listed in Schedule 3 must already have a legal mandate to receive this information through enabling legislation or other means.