"...and no patience."
In 2374, Yelgrun was sent to negotiate with a group of Ferengi for the safe return of Ishka, the paramour of Grand Nagus Zek, in exchange for Keevan, a Vorta who had been captured by Starfleet several months earlier. Though outwardly affable, Yelgrun would quickly lose patience and become cold and humorless (even by Vorta standards), having no qualms with threatening anyone he felt was wasting his time.
He agreed to meet Quark and his team on the abandoned space station Empok Nor, but he brought along an entire platoon of Jem'Hadar guards as protection against the six Ferengi. Yelgrun quickly got annoyed by the Ferengi's attempts to stall, however. Nevertheless, he agreed to send all of his Jem'Hadar (save two guards) away from the station as a gesture of goodwill (and to even the odds to keep the Dominion from getting the drop on the Ferengi).
Yelgrun may have spent time forming somewhat of a friendship with Ishka. She was seen giving him some financial advice, and waved good bye to him during the prisoner exchange.
The Ferengi had ideas other than a simple prisoner exchange, however. Yelgrun was tricked into exchanging Ishka for Keevan's animated corpse, thanks to some improvised engineering on the part of Nog, and the two Jem'Hadar guards protecting him were killed. Yelgrun himself was captured and taken back to Deep Space 9 to be handed over to Starfleet as a gift in thanks for allowing them to use Keevan for the prisoner exchange. (DS9: "The Magnificent Ferengi")
"Family. You understand."
"Not really. I was cloned."
- - Quark and Yelgrun
"I know, I know: You hate us."
- - Yelgrun and Quark
"Then you're going to tell your helmsman to head back to Dominion territory, warp nine."
"That would leave me stranded here."
"For a few days."
"I see. And by the time they return, you'll be long gone."
"That's the idea."
"On the other hand, I could have my Jem'Hadar storm the Infirmary and kill you all."
"I like our plan better."
- - Quark, Yelgrun, and Rom
"Seventy five hundred lots of hipicate futures?"
"The hipicate root is very versatile. It's used in certain medicines, defractive optics, and even some beauty supplies. Here, feel how smooth my head is. Cream of hipicate. I apply it twice a day. You see, a diversified financial portfolio can mean greater profits and healthier looking skin."
"I'd love to hear more, but if your son doesn't show up soon, I'm afraid I'm going to have to kill you."
- - Ishka and Yelgrun
"And I thought the Breen were annoying."
- - Yelgrun
"What have they done to him?"
- - Yelgrun, after seeing Keevan's animated corpse during the exchange
Yelgrun was played by actor and musician Iggy Pop.
The Star Trek Encyclopedia (3rd ed., p. 684) describes Yelgrun as simply "a Vorta official".
Producer Ira Steven Behr was a big fan of Iggy Pop and had previously tried to book him the role of Grady in "Past Tense, Part II", but the singer was unavailable at the time. However, when Pop dislocated his shoulder during a performance several months prior to "The Magnificent Ferengi", he was forced to take some time off for recuperation, allowing him the opportunity to take his short role in the episode. (Star Trek: Deep Space Nine Companion (p. 516))
As he was such a big fan of the artist, Behr made a point of visiting the set during production of the episode, which was something of a rarity due to his busy schedule. "For Iggy I would not be denied!" Behr joked. "I was a happy boy." Similarly, Hans Beimler recalled, "Ira was thrilled! For cryin' out loud, Iggy Pop has been a hero of his for years. I've heard about Iggy Pop since I've known him. I've seen Iggy Pop posters in his home. What can I say? The man was in heaven" (Star Trek: Deep Space Nine Companion (p. 516))
Though he was excited to have Pop onboard for the episode, Behr did have concerns that the character perhaps wasn't the best match for the singer, known for his wild stage presence. "I knew that the role was going to be tough for Iggy, because he's a very kinetic performer", Behr commented. "His physicality is certainly part of who he is, and unfortunately we cast him as a Vorta, one of the most immobile of characters." (Star Trek: Deep Space Nine Companion (pp. 516-517))
While filming his appearance, Pop was still suffering from the effects of his shoulder injury. As Behr recalled, "You could see that he clearly was uncomfortable for all the hours he had to be there on set, but he never complained." (Star Trek: Deep Space Nine Companion (p. 517))
Speaking of his performance in the episode, Behr thought Pop "really got that demented quality the Vorta have, like Weyoun has-think Caligula! He was just a delight." (Star Trek: Deep Space Nine Companion (p. 517))
Two identical Vorta costumes consisting of long-sleeved tunics with pleated shoulders and dark-green boucle, overall-style trousers were originally made for Iggy Pop but instead worn by an unnamed Vorta in "What You Leave Behind". They were later sold off in the It's A Wrap! sale and auction for US$665.00 and $1224.99 respectively, and with name tags that still read "Iggy Pop".   
The first edition card in the Star Trek Customizable Card Game spells Yelgrun's name incorrectly as "Yelgren". It also gives his Vorta rank as "Overseer" and describes him as "a 'matter-of-fact' Vorta" with a skill in music, most likely a reference to Iggy Pop's musical career. The spelling was later corrected in the second edition card.