Much like turtles, sharks do not die of old age; it is only due to other factors such as disease, injury, and human interference that these creatures die at all. Additionally, it is suggested that as they age, sharks become more, not less, resistant to disease, making it even harder for them to die unless a predator gets the best of them.
Giant tortoises are living much longer than any other known animal and it is not likely that any other animal will outlive them. There is no reason for animals currently existing to be living longer than normal, and in fact due to environmental and other factors animals may actually be living shorter lives than in the past. The lifespans of animals will not be increasing, therefore, none can expect to outlive the giant tortoise.
The giant tortoise has to be the longest living animal on the Earth. Some of the giant tortoises can live up to 255 years. This is much longer than most any other animal can live. These tortoises are the only animals that have the capability of being able to live and function for so many years. Every other animal's body will eventually wear out long before they reach such an old age. In short, no other animal will likely outlive them.
I don't think any other animal on the planet could sustain a 255 year life span. The creaking of bones, arthritis, not being able to run away from predators would surely put a damper on those hopes. Although, the more I think about it, there may be other animals having long lives. We may just not have stumbled across them yet. We really need to study the giant tortoises because they may have found the fountain of youth.