Adan joined the Armored Corps in 1949 and founded the first Sherman tank unit in the IDF. During the 1956 Suez War, Lieutenant Colonel Adan commanded the 82nd battalion of the 7th Armored Brigade in the Sinai, defeating several Egyptian forces in the region. After the war he became the operations officer of the corps, then the commander of the 7th Brigade and the Armored Corps School. During the June 1967 Six-Day War, Adan was the deputy commander of the Armored Corps and of the 31st Armored Division, fighting again in the Sinai. On 10 March 1969, he became the commander of the Armored Corps.
Major General Adan was defending the northern portion of the Israeli defense along the Suez Canal when the October 1973 Yom Kippur War broke out. As the commander of the 162nd Division, his division suffered severe losses from 6 to 8 October, in repeated attempts to stop the Egyptian attack and push it back across the canal. Later on during the war he led his unit across the canal into Egyptian territory just north of the Great Bitter Lake, during Operation Stouthearted Men. He then maneuvered his unit southward to Suez City, where his unit surrounded the Egyptian Third Army.
From 1974 to 1977 he served as the Armed Forces Attaché at the Israeli embassy in Washington, DC.