Look up the stuff David Sinclair is doing with his team. They are already rejuvenating and regrowing severed optic nerves with Yamanaka factors in mice and are preparing to start human trials.

It's not rock-solid that this is going to happen for the whole body soon, but some truly breakthrough things are happening right now in this field, nothing like the previous decades.

That doesn’t solve the issue that the passengers will need to live on the ship for a thousand years, even if their relatives will be on Earth for twice as long.

Even a very big ship can be boring after a sufficiently long time.

https://old.reddit.com/r/longevity has a lot of links to various articles and papers, and I also collect relevant videos and talks into a playlist: https://www.youtube.com/playlist?list=PLLvA7pB41pDk27XOjqbXi...