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I've asked AI to list all the prominent Jєωιѕн producers, directors, actors, and actresses in the Star Trek franchise.

Producers / showrunners

• Rick Berman — Probably the most consequential producer after Gene Roddenberry. He effectively ran the franchise through the TNG/DS9/Voyager/Enterprise era and executive-produced several films. Berman was born into a Jєωιѕн family. 
• Alex Kurtzman — The central executive/producer behind the modern streaming-era franchise: Discovery, Picard, Strange New Worlds, Starfleet Academy, etc. He was born into a Jєωιѕн family. 
• Michael Piller — One of the architects of The Next Generation at its creative peak, co-creator of Deep Space Nine and Voyager, and writer of Star Trek: ιnѕυrrєcтισn. Piller explicitly described himself as Jєωιѕн. 
• J. J. Abrams — Producer/director of the 2009 reboot and producer of Into Darkness and Beyond. His Jєωιѕн background is well docuмented. 
• Harve Bennett — The producer largely responsible for reviving the film franchise after the troubled reception of The Motion Picture. He produced The Wrath of Khan, The Search for Spock, The Voyage Home, and The Final Frontier, and was born Harvard Bennett Fischman into a Jєωιѕн family. 
• Ira Steven Behr — Showrunner and executive producer of Deep Space Nine, and one of the most important creative voices in Trek history. Born into a Jєωιѕн family. 
• Akiva Goldsman — Executive producer/co-creator of Strange New Worlds, producer on Discovery and Picard, and also a writer/director within the franchise. He was born to Jєωιѕн parents and has described being raised in a culturally Jєωιѕн household. 
• Robert H. Justman — One of the crucial original-series producers and later a producer on the first season of TNG. He worked closely with Roddenberry during the creation of the original show and was born into a Jєωιѕн family. 
• Herbert F. “Herb” Solow — Desilu executive who played an enormous role in getting the original Star Trek developed, sold to NBC, and produced. Born into a Jєωιѕн family. 
• Fred Freiberger — Producer of the third season of the original Star Trek. Contemporary Jєωιѕн retrospectives identify him among the original show's Jєωιѕн producers. 

There are others, but those are probably the major names where both the Trek contribution and Jєωιѕн background are well established.

Directors
There is quite a bit of overlap here because several important producers and actors also directed Trek.

• J. J. Abrams — Directed Star Trek (2009) and Star Trek Into Darkness. Probably the most internationally famous director on this list. 
• Leonard Nimoy — Directed Star Trek III: The Search for Spock and Star Trek IV: The Voyage Home. His success as a director established the precedent for Trek actors moving behind the camera. Nimoy was raised in an Orthodox Jєωιѕн household. 
• Nicholas Meyer — Directed Star Trek II: The Wrath of Khan and Star Trek VI: The Undiscovered Country and was heavily involved creatively with The Voyage Home. Born into a Jєωιѕн family. In terms of influence on the Trek films, he is enormous. 
• Akiva Goldsman — Has directed episodes of Discovery, Picard, and Strange New Worlds, including the Strange New Worlds premiere, in addition to his producing and writing work. 
• Corey Allen — Veteran television director who directed episodes of The Next Generation and Deep Space Nine; he is included in biographical listings of Jєωιѕн American film directors. 

If we're ranking importance specifically to Star Trek rather than general fame, I would probably put Nimoy and Meyer ahead of Abrams.

Actors

• William Shatner — James T. Kirk
   Easily one of the two most iconic Jєωιѕн actors associated with the franchise. Shatner grew up in a Jєωιѕн household in Montreal, attended Hebrew school and Jєωιѕн camps, and has spoken extensively about his Jєωιѕн identity. 
• Leonard Nimoy — Spock
   Perhaps the single most culturally significant Jєωιѕн influence on Star Trek. Nimoy was the child of Yiddish-speaking Ukrainian Jєωιѕн immigrants and grew up Orthodox. Most famously, he adapted the Vulcan salute from the hand gesture used during the priestly blessing by the Kohanim. 
• Brent Spiner — Data
   One of the principal stars of The Next Generation and its four feature films, later returning in Picard. Jєωιѕн retrospectives of the franchise regularly identify Spiner among Trek's major Jєωιѕн actors. 
• Walter Koenig — Pavel Chekov
   Major original-series cast member and participant in the original-cast movies. Koenig is from a Russian-Jєωιѕн family. 
• Anton Yelchin — Pavel Chekov
   Played Chekov in all three Kelvin-timeline films. He was born in Leningrad to a Russian Jєωιѕн family that emigrated to the United States when he was an infant. 
• Armin Shimerman — Quark
   One of the central cast members of Deep Space Nine. Shimerman has publicly discussed being Jєωιѕн, including his unease about whether certain aspects of the Ferengi could be interpreted as antisemitic stereotypes. 
• Wallace Shawn — Grand Nagus Zek
   Recurring Deep Space Nine character and a very recognizable actor outside Trek as well. Jєωιѕн sources include him among the franchise's prominent Jєωιѕн performers. 
• Mark Lenard — Sarek
   Spock's father and one of the most important recurring characters across the original series, films, and TNG. Lenard was Jєωιѕн. 
• David Cronenberg — Kovich/Daniels
   Much more famous generally as the director of The Fly, Videodrome, Dead Ringers, etc., but he became a substantial recurring character on Discovery, rather than merely doing a cameo. 
• Jason Alexander — Kurros
   The Seinfeld star guest-starred as Kurros in Voyager's “Think Tank.” His Jєωιѕн identity is well known, although his Trek role was only a guest appearance. 
• Saul Rubinek — Kivas Fajo
   Played Data's obsessive collector/kidnapper in the well-regarded TNG episode “The Most Toys.” Rubinek comes from a Polish-Jєωιѕн h0Ɩ0cαųst-survivor family.

There are also a number of Jєωιѕн male guest actors who would belong on a truly exhaustive list, but at that point we'd move from “prominent” into hundreds of individual Trek credits.

Actresses
The female list is shorter in terms of principal-series cast members, but there are several very recognizable names.

• Winona Ryder — Amanda Grayson
   Played Spock's mother in Star Trek (2009). Ryder publicly identifies as Jєωιѕн, although she is not religious; her father's family is αѕнкenαzι Jєωιѕн and she has spoken about relatives who died in the h0Ɩ0cαųst. 
• Carol Kane — Pelia
   Recurring as Enterprise chief engineer Pelia in Strange New Worlds. Kane is one of the most recognizable character actresses of her generation and comes from a Jєωιѕн family. Her Trek role is considerably larger than a cameo. 
• Sarah Silverman — Rain Robinson
   Played scientist Rain Robinson in Voyager's two-part “Future's End.” Silverman is of αѕнкenαzι Jєωιѕн descent and publicly identifies with her Jєωιѕн background while describing herself as nonreligious. 
• Mia Kirshner — Amanda Grayson
   Played Spock's mother repeatedly on Discovery. Her father is of Polish-Jєωιѕн ancestry and her mother is a Bulgarian Jєωιѕн immigrant. 
• Bebe Neuwirth — Lanel
   The Cheers/Frasier star appeared in the TNG episode “First Contact.” She was born into a Jєωιѕн family and describes herself as a cultural Jew, although she wasn't raised religiously.