I’m happy to help. To stem something means to stop the spread or development of something undesirable. In this context, playing an important role in stemming abuses means UNESCO had a role in stopping the spread of harmful aspects of the international trade in cultural artifacts.
We know the author of the passage would agree with this statement based on lines 13 - 25 about the UNESCO doctrine.
I hope that helps! Please let us know if you have further questions.
