After one particular decision in Star Trek: Deep Space Nine, Worf (Michael Dorn) should not have been able to become captain of the USS Enterprise. For most of Star Trek: The Next Generation's seven seasons, Lt. Worf serves as the security chief on the USS Enterprise-D under the command of Captain Jean-Luc Picard (Patrick Stewart). After TNG came to a close, Worf transferred to DS9, where he truly came into his own as a character and starship captain. Worf serves as the strategic operations officer on Deep Space Nine, coordinating Starfleet's activity within the Bajoran sector.
As the most senior officer under the leadership of Captain Benjamin Sisko (Avery Brooks) on DS9, Worf takes over command of the USS Defiant when Sisko is not in command of the ship. Initially built as a warship to defend against the Borg, the Defiant proves vital in the Dominion War and allows Worf to prove himself as a starship commander. Although Worf was never shown onscreen as the official captain of the Enterprise, he took over command of the Enterprise-E after Picard accepted a promotion to admiral.
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Worf ultimately remains loyal to Starfleet throughout TNG and DS9, but he occasionally makes choices based on his Klingon sense of honor and loyalty. In DS9 season 6, episode 16, "Change of Heart," the newly married Worf and Lt. Jadzia Dax (Terry Farrell) are sent on an important undercover mission to meet with a Cardassian defector named Lasaran (Todd Waring). Lasaran reportedly has valuable military intelligence that could aid the Federation in the Dominion War. As Jadzia and Worf trek through the jungle to rendezvous with Lasaran, Jadzia is seriously injured by a Jem'Hadar soldier.
Worf has one other mark on his service record: in TNG season 4, episode 7, "Reunion," Worf kills the Klingon Duras (Patrick Massett) in a duel to avenge his mate, K'Ehleyr (Suzie Plakson).
Although Worf initially agrees to leave Jadzia behind to complete the mission, he later changes his mind and returns just in time to save her life. Because Worf prioritized Jadzia's life over the mission, Lasaran dies before he can get his information to the Federation. After Worf returns to Deep Space Nine, Captain Sisko tells him that this event will go on Worf's service record and that "they'll probably never give you a command of your own after this." However, despite this blemish on his resume, Worf does eventually gets his own command, on the USS Enterprise, no less.
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At the end of DS9, Worf becomes the Federation Ambassador to the Klingon Empire until he rejoins the crew of the Enterprise-E in Star Trek: Nemesis. After the events of Nemesis, Worf was the only logical choice to take over as captain of the Enterprise to keep the ship in the TNG family. Thematically, it simply made more sense for Worf to be a captain in Star Trek: Picard season 3 than it did to honor a line of dialogue from one 20-year-old episode of DS9.
There are several in-universe possibilities as to why Worf's decision to save Jadzia did not prevent him from receiving a command. For one, Captain Sisko understood Worf's choice and even acknowledged that he would have done the same thing if it had been his wife in that situation. It's possible that Sisko vouched for Worf and emphasized all the positive things he did throughout his time on Star Trek: Deep Space Nine. Admiral Picard, too, could have spoken out in Worf's defense, and he likely held significant sway when it came to choosing the next captain of his beloved Enterprise.