To prolong venerable animals from dying of old age you can care for them. To start caring stand next to the animal, right click the animal and select ''Care for''. If you start caring for that animal you'll get the message:
You now care specially for Aged fat Tearbabe, to ensure longevity. You may care for 1 more creatures.
Hostile creatures must be tamed first before they can be cared for.
The amount of animals you can care for is limited by the animal husbandry skill of the player. If you can't care for more animals you'll get the message