This page contains information regarding Star Trek: Discovery, and thus may contain spoilers.
"No, but I know anger. It's a wonderfully productive emotion."
Tarka showed signs of a genius-level intellect at an early age. He felt he was never understood growing up on Risa, believing he was "surrounded by idiots". In his first scientific experiment at the age of five, he atomized a live caracal to prove a theory.
Tarka was once enslaved by the Emerald Chain and implanted with a control device on the back of his neck. He had been employed by Osyraa to seek out an alternative to dilithium in the wake of the Burn, and was paired with another scientist who became a close friend. Inspired by his friend's "relentless optimism", Tarka began looking into alternate universes, and together they found one where there was no war, no Burn, no Emerald Chain to enslave them. The two men eventually determined exactly how much power they would need to cross the dimensional veil. Eventually, Tarka escaped from the Chain, but his friend did not, though both made a promise to one another to meet in the alternate universe they had found together. He kept the scar left behind after his control device was removed, as a reminder of his grief.
By 3190, Tarka was considered an expert at the leading edge of both Federation and non-Federation technology, and headed a number of scientific endeavors for the Federation. One project of particular interest to the Federation was the next generation of the displacement-activated spore hub drive, based on Commander Paul Stamets' work aboard the USS Discovery. Tarka worked with ex-Emerald Chain scientist Aurellio, who acted as a middleman between him and Stamets, as Tarka always claimed to be "too busy" to speak to Stamets directly.
Following the discovery of the Dark Matter Anomaly, an artifically created phenomenon of immense power, Fleet Admiral Charles Vance requested Tarka's services as an advisor to Starfleet to counteract the threat. Tarka boarded the Discovery to work in concert with Stamets. Based on previously gathered data, Tarka theorized that the DMA had been tunneled through spacetime by its unknown creators, and proposed creating a scale model of the device believed to be controlling the anomaly and generate a miniature DMA inside Discovery. Though both he and Stamets were convinced the model would provide the answers they sought, Captain Saru aborted the experiment before the containment field around it failed and threatened the ship. Nevertheless, based on the model data, Tarka postulated that the energy source for the DMA was equivalent to that of a hypergiant star. (DIS: "The Examples")
During a summit meeting with the various members of the United Federation of Planets and their allies, Tarka interrupted the meeting, talking down various members in their failures in either damaging or studying the anomaly before revealing he had a plan to deal with it: with the aid of Discovery, they could drop a special weapon inside a safe spot within the DMA and detonate it, dissipating it. Realizing that it would use an isolytic burst to do so, Captain Michael Burnham quickly tried to shoot the idea down, noting it could damage subspace and prevent warp travel. However, Tarka had a surprising ally in the form of Cleveland Booker, Burnham's boyfriend and the last known surviving Kwejian, who Tarka knew was capable of navigating with a spore drive; Booker, vengeful at the loss of his homeworld, believed Tarka's plan was the only one that made sense. After the summit voted instead to pursue peaceful first contact with the unknown species behind the DMA, Tarka stole the prototype for the next-generation spore drive and installed it on Booker's ship, and Booker used it to jump away from Discovery. (DIS: "...But to Connect")