Prior to Israel's independence, he served with the Palmach, an elite formation within the Haganah paramilitary force of the Yishuv community in British Mandatory Palestine.

[4][3][5] In 1943, he joined the Palmach, an elite force of the Haganah paramilitary organization that operated on part of the Yishuv community in British Palestine.

During the Suez Crisis of 1956, he commanded the 82nd battalion of the 7th Armoured Brigade in the Sinai Peninsula, decisively defeating Egyptian forces in the region.

Adan was defending the northern portion of the Suez Canal in the Sinai—occupied by Israel in its entirety during the 1967 war—when the Fourth Arab–Israeli War broke out in October 1973.

From 1974 to 1977, he served as the military attaché at the Embassy of Israel in Washington, D.C.[5] Adan was a co-founder of the kibbutzim of Nirim and Gvulot, located in the Negev Desert near the Palestinian Gaza Strip.