What does Kimki do upon reaching safety?
I am not entirely sure what you are looking for from the wording of the question. However, I can tell you that Kimki is chosen as the new leader of the tribe after Karana's father is killed in the battle with the Aleut hunters. He immediately begins assigning tasks to each of the tribe members who remain alive, to help them survive the coming winter with so many fewer people to help.
The following spring, Kimki decides to take a canoe and try to find a land to the east that he remembers from his boyhood. His plan is to check out the new place and make it ready for the others. The tribe waits all through that spring and summer, but Kimki does not return.
The following spring, a ship arrives on the Island of the Blue Dolphins. It is not Kimki, but a group of white men whom Kimki has sent to get the remaining members of the tribe and take them away from Ghalas-at.