Kakashi was the hokage, so he has no action roles. However he did rally the other three kage to convince raikage to hold off destroying the moon for an hour. He also believed that the moon falling was connected to the kidnapping of Hanabi (it was not outright stated to the characters until after they were on the moon.) Kakashi also evacuated the village and stayed behind with select members in an attempt to destroy the meteor, showing a lack of fear in the face of potential destruction. And all this time, when characters questioned why he had faith, he answered simply that it was just his personal intuition (showing how much his words can be taken as truth through his experiences)
Ultimately, Kakashi was a hokage that did not need to fight for himself because all of his subordinates were highly capable.
