It's always interesting when worlds collide. Early in the 1980s, a show called "Cheers" started airing episodes. It became a smash hit, ran for 11 seasons, and went out on top. It launched numerous stars like Ted Danson and Woody Harrelson while bringing a whole new crop of actors to the forefront. The show would see their cast members go on to feature in shows and films like Matilda, Toy Story, Look Who's Talking, Happy Gilmore, and more.
The show was so successful it launched a spinoff called Frasier, featuring a core character from the original series, Frasier Crane, played in both shows by Kelsey Grammer . It was an incredibly rich and robust show that contributed greatly to the pop culture zeitgeist of its time. It's also a backbone for Star Trek actors.
The show helped a lot of names get on Star Trek, and in return, many Star Trek actors would appear in later seasons of Cheers and its spinoff. Brent Spiner, Patrick Stewart, Kristie Alley, Nana Visitor, Kate Mulgrew, René Auberjonois, and numerous others have all appeared on the Cheers universe of shows.
Heck, even Grammer would have a brief foray into Star Trek.
Yet, to this date, a lot of people don't know why there was so much talent cross-over. Well, for starters, they're both Paramount shows. They were both produced by some former arm of the Paramount Global brand. Star Trek was produced by Paramount Domestic Television, while Cheers was produced by Paramount Network Television, the same as with Frasier. Though Frasier would later also be produced by the PDT as well.
The three shows also shared studio space. Making it very easy for a member of either show to walk across the set and pick up an extra paycheck rather easily. Since not every actor is required for that given day of shooting, there are often opportunities for actors to pick up extra work. Which is the case here.
It appears as though the franchise developed a relatively strong bond, as both shows would reference one another. In Deep Space Nine, the alien Morn was named after Cheers character Norm and was known to be quite chatty just like Norm (though Morn was never seen speaking on screen). Later on, Frasier would feature a character named Noel Shempsky who was obsessed with Star Trek.
A fitting role for the character, as his actor, Patrick Kerr, appeared on Star Trek: Voyager in the episode "Persistence of Vision".
The interconnectivity between the shows and universes is profound and vast, and it just goes to show you how much proximity to one other does contribute to how our life evolves.