A radiocarbon dating study has determined that Greenland sharks can live for at least 272 years [arstechnica.com] (392 ± 120):
Because Greenland sharks lack bones—they're cartilaginous fish—conventional methods of tracking growth, like carbon dating of bones, won't work. Instead, the team used a modified radiocarbon dating technique that has worked before on other boneless animals: tracking the chronology of the eye lens. The eye lens nucleus is composed of inert proteins. The central portion of the lens is formed during prenatal development, and during growth, the tissue retains the original proteins, which were largely made before birth.
As a result, carbon-dating these proteins can help determine how long ago the shark was born. For this work, researchers performed radiocarbon dating on the eyes of 28 female sharks that were collected in Greenland during scientific surveys that took place between 2010 and 2013. According to the radiocarbon dating, these sharks live at least 272 years.
[...] In addition to determining longevity, the scientists wanted to determine the age at which Greenland sharks begin to reproduce. Through analysis of sharks that did not exhibit the "bomb pulse" radiocarbon indicator, the team determined that the reproductive age of the sharks was at least 156 ± 22 years, based on other results that indicated females only start reproducing once they reach four meters in length.
This investigation reveals that the Greenland shark is among the longest-lived vertebrate species, with a life expectancy exceeded by only one other ocean dweller (a species of whale). Since it takes them more than a century to reach reproductive age, conservation efforts are important to help keep this population from dwindling.
Eye lens radiocarbon reveals centuries of longevity in the Greenland shark (Somniosus microcephalus) [sciencemag.org] (DOI: 10.1126/science.aaf1703)