One of the books does mention baby skin for a capsuleer that got podded, one of the Gallente pilots flying escort to a certain Nyx. Other than that, no mention of aging or the reversal of aging, but I'd assume that capsuleers with enough money can have clones which make the most advanced plastic surgery pale in comparison - and plastic surgery is damn advanced in New Eden (full-body replacement except neural system, while the patient is conscious). Re-growing limbs has been mentioned (a certain Amarrian Heir, who happened to step out of what is allowed to him and was punished a kind of eye-for-an-eye punishment - but happened to have wronged perhaps a few thousand people).
Naturally, there might be psychological issues, if you modify your body too much - I'd at least assuming that waking up as someone who isn't you might be traumatic.
I assume that the oldest person currently alive is King Khanid II of the Khanid Kingdom. He competed with the late Emperor Heideran VII (the old frail guy) for the Imperial Throne, and lost. Usually losing that game means you commit suicide, but Khanid (assumedly quite young by Amarrian royal standards, perhaps a hundred years old or so) decided to take his estates and secede, instead. And he's still ticking. The Kingdom has had contact with the Gallente Federation for perhaps a hundred years or so, and the King has seen fit to get a former Gallentean pop star as a personal slave. (As this is older PF, I assume we are expected to think dirty.) Of course, the King is a special case, since he's likely kept going with the best Amarr and Caldari tech can provide (with possibly cloning - he's already given the finger to the Amarrian Orthodox customs of how to choose the Emperor, I assume the tabu of cloning royals doesn't mean much to him).
Cloning, however, is not necessarily a lightly taken endeavour. One chronicle has a person use jump clones as a personal teleportation device, but even when the tech is near perfect, there is an infinitesimally small chance that something goes wrong even in well-controlled situations (on a well-prepared operation in a hospital, in the hydrostatic capsule). In a hurried operation (personality-saving emergency cloning to escape a dying body) things can be expected to go wrong.