Star Trek: The Next Generation has managed to repeat this one unfortunate mistake with both Captain Kirk and Spock. If there is something in the Star Trek franchise that fans love as much as the trio of Captain Kirk, Spock, and Dr. Leonard Nimoy, if not more, it is Captain Kirk's USS Enterprise.
After the unprecedented success of Star Trek: The Original Series, Star Trek: The Next Generation was released in 1987, and Gene Roddenberry decided to never directly mention the USS Enterprise crew, especially Kirk or Spock, in an attempt to make sure that the show stood by itself and was not just a spin-off of the original.
This rule, even though it relaxed over time, meant that both Spock and Kirk never visited Captain Jean-Luc Picard's Enterprise-D. Here's what happened.
Captain Kirk and Spock, unfortunately, never set foot on Star Trek: The Next Generation's Enterprise-D

When Star Trek: The Next Generation was in its starting stages, the creator, Gene Roddenberry, wanted it to stand completely apart from the original series, so he directed the writers of TNG to never mention the Enterprise crew, including Spock or Kirk, by name in the show. It was in this show that Patrick Stewart's Captain Jean-Luc Picard, the celebrated Starfleet officer, was assigned to the Enterprise-D with his crew.
As Star Trek: The Next Generation grew in its popularity, Roddenberry's rules to avoid mentions of the Original Series' crew grew more relaxed, and Picard eventually went on to encounter and interact with Captain Kirk and Spock on different occasions. Even other characters from Star Trek: The Original Series make appearances on the show. However, despite their appearances on the show, Spock or Captain Kirk never visit Picard's Enterprise-D, despite it being Kirk's USS Enterprise's successor.
Captain Picard meets Spock for the first time in Star Trek: The Next Generation's Season 5 Episodes 7 and 8, titled Unification. The Federation employs Captain Picard to track an ambassador who had suddenly disappeared without a trace and was then spotted on the planet Romulus weeks later. The Federation is concerned that this ambassador has defected and wants Picard to track him down. When shown an image that intelligence has found, Picard discovers that the missing ambassador is none other than Spock.

Eventually, Captain Picard and his Enterprise-D crew discover Spock, who is on a personal mission to unite the Vulcans and the Romulans. Captain Picard is also forced to be the one to tell Spock that his father, Sarek, with whom Picard shared a mind meld, has died. Even though Spock is majorly present in the two-part episode of Star Trek: The Next Generation, he never actually visits Picard's Enterprise-D, as Picard and his Lieutenant Commander Data travel to Romulus on a Klingon ship so that they can stay cloaked in their mission to track Spock.
As for Captain Kirk, Picard meets him in Star Trek Generations, a crossover between Star Trek: The Original Series and Star Trek: The Next Generation. At the beginning of Generations, Captain Kirk is presumed to be dead after his voyage in the USS Enterprise-B. However, Picard later discovers that Kirk is alive and living in Nexus, a point in space where even time flows differently.
It is revealed that the incident, which was assumed to be the cause of Kirk's death, had actually thrown him into the Nexus. Captain Kirk then joins Captain Picard and the rest of his crew in their fight against the villain Dr. Tolian Soren, who was also trying to get into the Nexus. Unfortunately, Kirk dies in this fight against Soren and never gets to visit Enterprise-D.

It is truly a shame that Star Trek: The Next Generation repeated the same mistake with Spock and Captain Kirk, and they never get to visit the Enterprise-D, even though it was the true successor to their beloved USS Enterprise.
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