Based on the context given and the timeline of major civilizations in Egypt during ancient times, the key event that seems to be missing in the New Kingdom period (1550–1069 BCE) is related to the Hittites and Mitannians in Palestine.
The New Kingdom was characterized by military campaigns and interactions with neighboring powers, including conflicts with the Hittites, particularly notable in the Battle of Kadesh. Thus, "Hittites and Mitannians in Palestine" would be the most appropriate response to fill in the missing military campaign for the New Kingdom.
So the answer would be:
Hittites and Mitannians in Palestine