lolkatz
Rav Kook taught Rav Hutner in his earlier years studying in Eretz Yisrael. As time went on, Rav Hutner distanced himself from Rav Kook and his ideas (including Zionism). An example of this is when Rav Hutner halted the practice of hanging up a picture of Rav Kook in his Succah. He replaced it with a picture of the Chazon Ish in order to show he did not support the Zionism that followers of Rav Kook promoted.
In fact, there are no seforim by Rav Kook in Yeshivas Rabbeinu Chaim Berlin. While Rav Kook was certainly an influence on Rav Hutner as a student, he did not continue these ideals when he became Rosh Yeshiva of Yeshivas Rabbeinu Chaim Berlin.