Is it possible to get your animal companion killed? And if it is possible,, how can a Ranger get a new animal companion? By summoning, or by taming another beast? Is it just up to the game master?
Yes, you can get your animal companion killed. Nothing on your character sheet is permanent or "safe" (DW PDF version, p. 30):
"Prescriptive change" means that having Animal Companion on your sheet gives you an animal companion, but "descriptive change" means that when you get your animal companion killed, you lose the Animal Companion on your character sheet.
Similarly, descriptive change is how you get an animal companion again: you go and befriend another animal, so that it accompanies you as your companion.