Abraham Accords Cybersecurity Cooperation Act of 2023 This bill allows the Department of Homeland Security (DHS) to, in consultation with the Department of State, engage in activities to strengthen network defense and cybersecurity collaboration between Abraham Accords countries and the United States. This bill may not be construed to modify or expand any existing authority granted to DHS or the State Department. (The Abraham Accords are agreements to normalize or improve relations between Israel and four members of the Arab League: the United Arab Emirates, Bahrain, Morocco, and Sudan.)