Well, elephants were domesticated at some point right? War elephants were used in India and Thailand until 19th century I think. The trainers/riders were called Mahuts or something similar.
New pet? Or something that will call the mama? Elephants very rarely leave young behind. @Treant21
The problem in this case would be feeding it. Remember that a single mammoth earlier in the series was CONSTANTLY eating to sustain itself. The greenery just couldn't keep up. They were more like locusts than current elephants.
The 'regular' elephants that became war mounts were much smaller, and had much lower requirements on keeping it fed.