Why not..?

I am suggesting this as an alternative to the other two answers because, if the law clearly limits its applicability to specific circumstances, then it would be too broad to interpret the source phrase to address matters merely relating to or pertaining to the law. "Arising under this law" is also a good alternative. But in U.S. law, the phrase "subject to" unequivocablly limits the scope of the phrase precisely to those matters meeting the criteria for the law's applicability.

"governed by" sounds better than "subject to". I'm not sure why. Perhaps because I would think of people and companies being subject to laws, whereas matters are governed or covered by law/legislation. "legislation" sounds better to my English ears than "law" or "Act", although both would be acceptable.