Doctor Who and Star Trek are two of the longest-running sci-fi franchises of all time, and there is understandably a significant overlap between the two fan bases. While there have been several instances where the two sagas have collided, it has yet to happen in any notable way in live-action. Instead, those adventures have been reserved for comic books and other media. That said, Paramount and the BBC have been ramping up the clues in recent years that such a collaboration is set to hit the small screen.
Ncuti Gatwa's Fifteenth Doctor made a direct reference to visiting the Star Trek universe in 2024's "Space Babies." Then, in 2025, Star Trek: Strange New Worlds actually included a brief shot of the Doctor's TARDIS in "The Sehlat Who Ate Its Tail." A few episodes later, the season 3 finale included a coy line from Carol Kane's Commander Pelia that all but confirmed she had met the Doctor: "Remind me to tell you about the time I spent with a time-travelling Doctor I once knew."
Both Star Trek and Doctor Who make use of every sci-fi trope in the book, so it wouldn't be very hard to come up with a canonical way for the two franchises to crossover. In fact, it would probably be more of a challenge to narrow down the possibilities to one definitive way forward. It should be noted that such a crossover has not been confirmed by either the BBC or Paramount. That doesn't mean we need to ignore the teases. Let the speculation begin.

1. The Doctor could travel from the Doctor Who universe to Star Trek's Prime Timeline (or vice versa for a Starfleet vessel)
Star Trek is no stranger to a good old-fashioned multiverse story. While Doctor Who uses this specific trope far less frequently, it's still canonically possible for the characters to travel between realities. Therefore, it's more than reasonable to assume that the Doctor could end up piloting the TARDIS into a rift that spits him out in the Star Trek universe. Similarly, the same is also true for a ship like Captain Pike's (Anson Mount) USS Enterprise, which could experience a similar phenomenon that pulls it into the Doctor Who universe.
I give Captain Pike as an example here because it's Strange New Worlds that seems to be pushing most strongly for a Doctor Who crossover. Besides, Pike's crew has already been on some pretty quirky adventures, so Strange New Worlds would be the perfect vehicle to accommodate this storyline. Then again, with Doctor Who trying to reclaim its reputation after the divisive Disney era, maybe the BBC will be more eager to lead the way on this one. Regardless, Fifteen's wink in "Space Babies" to meeting Star Trek characters suggests something like this has already happened, or that he knows it's possible.
2. An iconic 2006 Doctor Who scene could have already set up the Star Trek crossover
This admittedly also revolves around the concept of the multiverse, but it requires reality hopping for both franchises. Perhaps the most well-known alternate reality in Doctor Who is the universe where David Tennant's Tenth Doctor experienced his tearful farewell with Rose Tyler (Billie Piper) in the season 3 finale. The reality has never been seen onscreen since, nor can it be easily accessed, but the potential of a Star Trek crossover suddenly makes it relevant again.
One of the biggest obstacles when navigating a crossover like this is figuring out how it'll impact both canons moving forward. Choosing one of the shows' primary settings as a staging ground could favor (or disadvantage) one side more than the other. So, what if Rose and Tennant's Meta-Crisis Doctor, who were left in THAT alternate universe, find a way to jump into another universe, and a Starfleet crew ends up in the same neutral universe after temporarily leaving the Prime Timeline behind?
This new universe would be a brilliant way for a compelling version of the Doctor (and Tennant) to return, as well as restoring Billie Piper to her role without that weird twist in Gatwa's final episode. Then, when the encounter with whatever Star Trek characters make the jump is done, all characters can return to their respective universes, and both franchises can move on. This way, there's no need for constant references to what happened. The main Doctor wouldn't even know it had taken place.

3. Star Trek can pay off Commander Pelia's obvious reference to the Doctor from Strange New Worlds
The beauty of Commander Pelia is that she is thousands of years old, and possibly even older than the Doctor. Her Lanthanite physiology has allowed her to live a long and fruitful life, so Strange New Worlds can show and discuss even fewer of her adventures than its other characters. Still, it's quite obvious she was talking about the Doctor in Star Trek, as it feels far too vivid a story to be a fun little throwaway line or a casual easter egg.
Strange New Worlds still has two full seasons to get through before it ends, so there will be numerous opportunities for the show to dedicate an episode (or two) to Pelia's meeting with the Doctor, which would happen via flashback. The multiverse bringing them together is one possibility, but the episode itself could opt for another avenue. Alternatively, the possible Doctor Who crossover with Star Trek could take the form of a special or feature-length production, which would allow Pelia and the Doctor to take center stage for substantially longer.
