5th Edition is deliberately vague about aging so as to avoid RAW pitfalls but in certain areas such as Timeless Body there seems to be an inherent contradiction: Monks cease to age and no longer require food or drink.
Now I've read that WotC considers this to be: "a "Ribbon", i.e. a neat ability with mostly story, rather than mechanical, applications.
Aside from the 8th level spell Clone there aren't many ways to be effectively immortal, but it seems like Timeless Body would provide it–except for the inherent contradiction of Monks no longer aging and not suffering from the debilities of aging–until they die of old age?!?!?
Best Answer
Timeless Body does not stop your natural aging
The text on Timeless Body says:
As a monk, they simply suffer "none of the frailty of old age," which means even as old people, they can still move like they were in their 20's. This makes sense when you consider the amount of old monks who can do flawless kung fu in media. They usually serve as mentors to the younger folk so that their secret techniques don't die with them.
In conclusion: Timeless Body still lets you age, and you may still die of old age naturally. However, due to your timeless body, you don't get the back pain or blurry vision that comes with senescence.