While investigating the mysterious Delta Triangle (a deep-space take on the myth of the Bermuda Triangle), where numerous ships have vanished without a trace over the centuries, the Enterprise is drawn into a conflict with a Klingon battle cruiser, which vanishes right in front of them. When two more Klingon vessels arrive and accuse Kirk of destroying their other ship, the Enterprise retreats into the triangle and is pulled into a pocket in space they can't escape.
Inside, they find a graveyard of ships, some which have been there for decades or even centuries. They also find their weapons don't work in this region. Kirk is transported before the council of a society called the Elysians, made up of the different species who have been pulled into this dimension over many centuries. They don't age because time moves at a near standstill in this pocket compared to normal space, and they've created a peace-oriented utopia where violence is forbidden.
Unclear is how this society can possibly work given that it appears to be made up of only a council chamber in a confined space of nothingness. (Where do they get food or resources? Are they on a ship, a planet, a space station?) The story is not interested in those details. It's more interested in Kirk's intention to escape this pocket of space-time, which the Elysians say isn't possible given its properties, which drain power from the ships within it. But Spock has a plan which involves allying with Kor, the captain of the Klingon vessel that was pulled inside the rift with them. By working together, they can combine their ships' use of power and escape.
This is essentially the same take that Voyager's "The Void" had on a similar story about ships being trapped in a bubble of nothingness. This story works for a lot of the same reasons (touting the values of teamwork and putting differences aside in the face of larger problems), and earns points for its basic storytelling competence. I find that I like TAS better when it's hewing closer to traditional Trek storytelling rather than (poorly) animated strangeness.
This story wouldn't be complete without Kor's duplicity after agreeing to Kirk's plan of cooperation, and his plan is to blow up the Enterprise with a planted explosive seconds after they escape the anomaly. Naturally, this backfires spectacularly, but as TAS goes, this feels more like TOS and less cartoonish than it could've.
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