R. Gershon Tannenbaum lists the Ashkenazic Chief Rabbis of Israel in his "My Machberes" column in this week's The Jewish Press (link):
Rabbi Avraham Isaac Kook, zt”l (1864-1935) Chief Rabbi of Jerusalem and prolific author, was appointed as Ashkenazi Chief Rabbi of (then) Palestine in 1921 and served until 1935;There is a three volume history of the Chief Rabbinate of Israel by R. Shmuel Katz: Ha-Rabanut Ha-Roshit Le-Yisrael: Shivim Shanah Le-Yisudah (Heikhal Shlomo, 2002).
Rabbi Yitzchok HaLevi Herzog, zt”l (1889-1959) previous Chief Rabbi of Ireland and author of Heichal Yitzchak, was appointed as successor to Rabbi Kook in 1936 and served until 1959;
Rabbi Isser Yehuda Unterman, zt”l (1886-1976) Chief Rabbi of Tel Aviv, was appointed Chief Rabbi of Israel from 1964 to 1973;
Rabbi Shlomo Goren, zt”l (1917-1994) former Chief Rabbi of the Israeli Defense Forces, served as Chief Rabbi of Israel from 1973 to 1983;
Rabbi Avraham Elkanah Kahana Shapira (born 1917) Rosh Yeshiva Mercaz HaRav and author of Even Ha’Ezel, served as Chief Rabbi from 1983 to 1993;
Rabbi Yisroel Meir Lau (b. 1937) Chief Rabbi of Tel Aviv served as Chief Rabbi of Israel from 1993 to 2003;
and Rabbi Yonah Metzger (b. 1953) Regional Rabbi of North Tel Aviv, was appointed as Chief Rabbi in 2003, and presently serves as the 7th Ashkenazi Chief Rabbi of Israel.