In Star Trek, when did Jean-Luc Picard (Patrick Stewart) take over from James T. Kirk (William Shatner) as Captain of the Enterprise? As every diehard Trekkie knows, Starfleet's most iconic starship didn't directly from Kirk to Picard in-universe. Kirk commanded the Starship Enterprise in the 23rd century and Picard was the captain of the Federation's flagship, the U.S.S. Enterprise-D, in the 24th century.
In the real world, Kirk was Star Trek's Captain from The Original Series in 1966 onward until his death in Star Trek Generations, while Captain Picard was the star of the spinoff series, Star Trek movie franchise.
Within the Star Trek timeline, Picard's Galaxy-class U.S.S. Enterprise-D launched in 2363 - 70 years after Kirk's final mission as Captain of the Constitution-class U.S.S. Enterprise-A as seen in Star Trek VI. (Christopher Pike. It's notable that despite his legendary missions spanning 33 years, Kirk's Enterprise was not the flagship of the United Federation of Planets, a distinction Picard's Enterprise-D received - in part because of the legacy of the Starship Enterprise.
Meanwhile, following the letters of the alphabet, there were two other Enterprises in the interim between Kirk and Picard. The Excelsior-class U.S.S. Enterprise-B was commanded by Captain John Harriman (Alan Ruck). The Enterprise-B launched in the flashback scene of Star Trek Generations, which was set in 2293; during its shakedown cruise around the solar system, the Enterprise encountered the Nexus, a ribbon of other-dimensional space, that pulled Kirk inside it. Kirk was presumed dead but he existed within the Nexus until he met Picard, and then the original Captain actually died saving the Veridian star system in the 24th century. But aside from Demora Sulu (Jacqueline Kim), the daughter of Hikaru Sulu (George Takei), as its helmsman, little else is known about the voyages of the Enterprise-B.
The Ambassador-class U.S.S. Enterprise-C has a much more fascinating story: Picard and his crew encountered his predecessor's ship in the classic Star Trek: The Next Generation episode "Yesterday's Enterprise". Commanded by Captain Rachel Garrett (Tricia O'Neil), the Enterprise-C fell into a temporal rift while fighting Romulan warbirds at a Klingon outpost in 2344. The Enterprise-C emerged 22 years later in an alternate timeline where the Klingons were at war with the Federation - a new reality the Enterprise-C's absence from the timeline created. With the help of Picard and the crew of the Enterprise-D, the Enterprise-C returned to the past, even though it was doomed to be destroyed in battle in order to properly set the timeline right. After the Enterprise-C was lost, Starfleet didn't commission another starship named "Enterprise" until the Enterprise-D was launched in 2363.
For his part, Picard had already served as Captain of the U.S.S. Stargazer when he took command of the Enterprise-D, which made him a seasoned leader, unlike Captain Kirk, whose first command was the original Enterprise. And yet, by the time the two Captains met in Star Trek Generations, Kirk was quick to remind Picard that "I was saving the galaxy while your grandfather was in diapers".
Fans don't yet know Star Trek: Picard will hopefully answer. Yet despite the other Captains of the Enterprise, only Kirk and Picard truly matter. Fans have spent decades arguing whether Kirk is better than Picard but they can be forgiven for assuming the Starship Enterprise ed directly from one to the other.