Whenever there is an Enterprise in a Star Trek movie or TV show, it's almost always at the heart of the story. However, there are exceptions to this. For example, Star Trek: Picard season 3's ending introduced the USS Enterprise-G to the franchise with Captain Seven of Nine (Jeri Ryan) as the ship's commanding officer, just as the show concluded. This revelation quietly set up the much-desired Star Trek: Legacy, but such a project has yet to receive the green light. Regardless, the franchise has arguably heard enough of the ship name, which could account for Legacy's delay.
Deep Space Nine's "Past Prologue" Was The First Episode With No Enterprise Whatsoever
Captain Picard kept the streak alive in Deep Space Nine's debut
Star Trek: The Original Series' cast got the franchise started in 1966 aboard the USS Enterprise-A. Captain James T. Kirk (William Shatner) and his crew embarked on countless adventures that all featured the famous vessel, and they continued to explore in the now-canon Star Trek: The Animated Series. After TOS ended, the TV branch of the franchise turned its attention to the USS Enterprise-D when Star Trek: The Next Generation began in 1987. All seven seasons of TNG adopted its predecessor's Enterprise-heavy approach, so it took until Star Trek: Deep Space Nine for this streak to come to an end.
The short crossover between Star Trek: The Next Generation and Star Trek: Deep Space Nine meant the latter began the year before the former ended. So, to aid in the transition between the shows, Stewart's Picard made an appearance in DS9's two-part pilot episode, along with his ship - the USS Enterprise-D. Therefore, it wasn't until Star Trek: Deep Space Nine season 1's "Past Prologue" that the franchise released an episode without an appearance from any Enterprise.
Star Trek's Relationship With The Enterprise Is More Sporadic Today
The Enterprise only shows up when required in Star Trek's modern age
"Past Prologue" marked a big turning point in the franchise, as it no longer became necessary to have an Enterprise in every episode. Of course, more episodes of Star Trek: The Next Generation did air after "Past Prologue," but the streak had already been broken by then. Star Trek: Voyager came next, which had a new ship to focus on, but then Star Trek: Enterprise retroactively installed the Enterprise NX-01 as the first Starfleet ship to canonically bear the name. In the saga's modern era, the Enterprise has continued that inconsistent pattern of appearances.
Star Trek returned with Star Trek: Discovery in 2017, and Captain Pike (Anson Mount) brought the USS Enterprise-A back at the end of season 1 and remained as part of the story for season 2. Mount went on to be central in Star Trek: Strange New Worlds, which brought the franchise back to its focus on ships named Enterprise. However, other projects like Star Trek: Prodigy, Star Trek: Lower Decks, and Star Trek: Picard either had no involvement or only passing dalliances with the most famously-named ships in Star Trek.