1883, set in the titular year, follows the great-grandfather of the main protagonist of Yellowstone which is set in the present day, so no one from the former is alive in the latter. The main connection is that both protagonists are part of the Dutton family, 1883 just shows the origins of that family as they move across America.

Subsequent series such as the upcoming 1923 follow the next generation of the Dutton family and I assume that there will be more series that continue this trend until they reach near-enough the present day.