In the context of the Russian space system, I asked the question What is different from the R-7 that launched Sputnik, to the Soyuz launcher used for Soyuz/Progress launches?
Thus we see that much of the current Soyuz booster has strong legacy ties back to the R-7 booster from the 1950's.
On the US side, what is the oldest legacy launcher in service?
Delta-4 uses a new engine and looses pretty much all of its Delta heritage.
Atlas-V uses almost nothing in common with the earlier Atlas versions. (Unless you count the Atlas 3, which also loses much of its commonality with the earlier Atlases, but is a stepping stone to Atlas-V).
The Space Shuttle would have been 30+ years old. We might say SLS using Shuttle components would continue the Space Shuttle longer if we stretch the definition.
To stretch the idea even further (to its own detriment) you could consider that the Merlin engine design is based on the Lunar Module Ascent engine design. But that seems like a two level stretch, a bridge too far in this context.
Capsule design, which of course has Apollo heritage, since how could SpaceX/Boeing ignore the tons of research papers NASA produced, but are not legacy in the sense meant here.
