In 2370, Gul Evek held the position of commanding officer in the Cardassian Fourth Order, assigned as representative and overseer of Cardassian affairs in the Demilitarized Zone. He was also commander of the Vetar, a Galor-class warship.
One of Evek's first missions as overseer in the Demilitarized Zone was to oversee the transfer of the former Federation colony on Dorvan V to Cardassian control. However, Evek arrived several weeks early while Starfleet was still in the process of evacuating the civilians on the planet. Evek's troops' presence was highly provocative, and precipitated a brief firefight with the Federation colonists.
However, rather than ordering more troops to "pacify" the colony, Evek ordered a withdrawal in the interests of preserving the peace treaty with the Federation. Evek confided in Jean-Luc Picard that he had lost two of his three sons during the Cardassian wars. In order to avoid a renewed war, Evek agreed to the controversial settlement in which Federation colonists on Dorvan V and elsewhere would be permitted to retain their homes under Cardassian rule. (TNG: "Journey's End")
Evek was contacted by Miles O'Brien from Deep Space 9 concerning an infestation of Cardassian voles on the station. Evek offered little help, sardonically suggesting that a Federation withdrawal from Bajor would solve their vole problems. (DS9: "Playing God")
At the start of the Maquis uprising against the Cardassian rule of the colonies in the Demilitarized Zone, Evek was responsible for capturing and interrogating William Samuels, a Maquis operative who was responsible for the destruction of the freighter Bok'Nor at Deep Space 9. Using the information acquired from Samuels, he confronted Federation colony leaders on Volan III and accused them of participating in an official Starfleet plot to secretly arm the colonists against the Cardassians – while at the same time the Central Command was arming its own citizens in turn. (DS9: "The Maquis, Part I")
On stardate 47941.7, The USS Enterprise-D came to the rescue of Evek and his crew when his ship was attacked by several Maquis ships. Evek and Picard exchanged words, each accusing the other of not doing enough to suppress the skirmishes in the Demilitarized Zone. (TNG: "Preemptive Strike")
Not much later, Evek arrested Miles O'Brien on charges of sedition against the Cardassian Union by secretly transporting a cargo of photon torpedo warheads aboard his runabout. Evek testified at O'Brien's trial that these warheads were destined for the Maquis, and were evidence of further Federation attempts to arm the rebel colonists against the Cardassians. In reality, the warheads had been planted by Evek's men as part of a Cardassian plot to discredit the Federation's policy in the Demilitarized Zone. (DS9: "Tribunal")
In 2371, Evek, while in command of the Vetar, pursued a Maquis raider, the Val Jean, piloted by Chakotay into the Badlands. The Vetar was struck by a plasma storm inside the Badlands and was disabled. (VOY: "Caretaker")
"Complete your mission. But remember, this is Federation territory, Gul Evek, and until that changes, these people are under my jurisdiction and I will protect them."
"Is that a threat?"
"It's a fact. Bear that in mind while you conduct your survey."
"I lost two of three sons in the war, Captain. I don't want to lose the last one."
"You've got the station, you've got the voles. By the way, their mating season begins in about six weeks."
"Thanks for your help."
"Gul Evek has tied the Maquis to this plot by quoting reliable sources. I think we deserve to know who these reliable sources are."
"Can you provide any details, Gul Evek?"
"I'm afraid that information cannot be revealed without risk to national security, Madame Archon."
"That's an acceptable answer."
"Maquis ship, this is Gul Evek of the Cardassian Fourth Order. Cut your engines and prepare to surrender or we will dest..."
Background information Edit
Gul Evek was played by actor Richard Poe.
Along with Quark, Morn, and Q, Evek is one of only four characters to appear in Star Trek: The Next Generation, Star Trek: Deep Space Nine, and Star Trek: Voyager. He is also one of a small number of characters to appear in Star Trek: Deep Space Nine prior to appearing in Star Trek: The Next Generation. The others were Julian Bashir, Quark, Morn, and Chekote.
The script for "Playing God" did not originally name Evek, simply referring to his part as "Cardassian Officer".  The final script for "Journey's End" describes Evek's introduction as, "His attitude is blunt and hardnosed, but he is not arrogant or obnoxious -- he's simply a Cardassian officer sent here to do a job and he means to do it." 
The decision to keep bringing back Evek for the Maquis arc was both a reflection on the actor's work and also to provide a sense of continuity for viewers by linking the three pre-Voyager episodes (and thereby reinforcing the backstory). "You want to have the opportunity for crossover and continuity," recalled David Livingston. "It's fun to do that with a character when you find somebody that's good in the part, like Evek and Admiral Nechayev. The audience enjoys it." (Star Trek: The Next Generation Companion, pp. 289, 298; Star Trek: Deep Space Nine Companion, p. 134)
Richard Poe's first scene to be shot was the one in which Evek tells Picard of his sons deaths in the previous Federation-Cardassian war, which Poe considered to be a very emotional one. Of the character, he recalled, "Evek has his shades of grey, moments of understanding, of detente, with the Federation. At other times he's imperious, and in one episode he was a real true killer. But he thinks with purpose, defending his people. They are bureaucratic and very strict... constructionists if you will, but luckily this character had a little bit of humanity at times too. Fun to play." That Evek's fate was never seen on-screen, Poe was of the opinion that he was killed while chasing Chakotay's raider in "Caretaker". 
It took three and a half hours for Poe's Cardassian makeup to be applied to him prior to shooting. 
Evek appears in a number of non-canon works.
In Book Two of The Badlands mini-series, Evek is in charge of preparing a trap for a planned Maquis attack on the space station Opek Nor, ordering Seska to frame Starfleet spy Tuvok for the mission's failure. Unfortunately for them both, their attempts fail and the Maquis mission is a success. Evek's status within the Cardassian Military is revoked, causing him to set out on a mission of revenge against the Maquis, culminating in the battle with Chakotay's raider. After his ship is subsequently damaged in plasma storms, he is rescued by the crew of Voyager but commits suicide shortly thereafter. The novel also reveals that he was a skilled poet and is one of the most respected Cardassian military commanders alive; to serve on Evek's ship is considered the high point of any Cardassian's career.
The novel A Stitch in Time has Evek surviving his battle with Chakotay's raider, eventually taking a prominent role within the Directorate Political Group on Cardassia shortly after the end of the Dominion War. At one point, during a meeting that Garak also attends, Evek calls Dukat a traitor, which elevates Garak's opinion of him.
In the alternate timeline of the Strange New Worlds short story "Gods, Fate and Fractals", Evek rejects further negotiations over Dorvan V and fires upon the Enterprise. This sparks a six-day conflict, dubbed the "Battle of the Border", after which the border is redrawn.
Evek is also featured in multiple editions of the Star Trek Customizable Card Game, one of which describes him as a "harsh interrogator".