Jack was a short tempered resident of the The Pines of Mar Gables Phase II condos in Florida and seemed to consistently have a grudge against Morty Seinfeld (Jerry Seinfeld's dad) and was the condo association vice-president under him. He was famous for shouting "Ahh!" while waving his hand down, which is often how he would end an argument with Morty.
He carried a Space Pen, the kind used by astronauts, which could write upside-down as seen in "The Pen." He showed it around and gave it to Jerry after the comedian complimented it, leading to consternation over whether it was a gift that should have been accepted. At the same time, Jack Klompus was the MC of an event that honors the condominium president. During the event, both of them get into a fight which results in Jack's dental plate getting broken as Jack vows to sue Morty. Morty and Jack continue their argument. Following the incident, Morty and Helen's neighbor Evelyn tells Helen and Morty that she can offer her nephew Larry to represent him in the case against Jack as he is a good lawyer.
In “The Raincoats,” Morty asked Jack to retrieve a box of leftover "Executive" raincoats from his garage and send them to him in New York. Because the garage was locked, Jack broke a window to get in, cutting his hand in the process. He neglected to fix the window, which allowed burglars to enter the Seinfelds’ home and rob them. Jack also sent them later in the day so as to save money on the express shipping fee and also simply tucked the flaps of the box instead of taping them, causing the coats to spill out of the boxes en route to New York.
When Jerry bought his parents a Cadillac with the money he received for a show in Atlantic City as seen in "The Cadillac, Part 1," Jack became suspicious of Morty, thinking he stole the money from The Pines of Mar Gables Phase II's treasury, using them illegally as board president. Although Jerry offered to provide a copy of the bill of sale for the car, Morty declined, saying it wouldn't help matters. Subsequently, Jack and the other board members voted to impeach Morty. The impeachment succeeded. In "The Cadillac, Part 2," Jack taunted Morty outside the restaurant stating that when Morty is impeached, he'll have plenty of time to drive around in his Cadillac. Upon Mabel Choate remembering that Jerry was the one who mugged her for her marble rye upon Jack calling her an "old bag," she changed her vote from against impeachment to in favor of impeachment. As a result, Herb dismisses Morty and swears in Jack as the new condo president as part of the second constitution of The Pines of Mar Gables Phase II.
In "The Money," Morty and Helen Seinfeld ended up selling the Cadillac to Jack for $6,000 and tried to give the money to Jerry, who bought it back from Jack for $14,000. Jack proceeded to crash the car in Alligator Alley in the Florida Everglades as he contacts Jerry about it where he even lost his astronaut pen. After handling the repairs for the Cadillac, Jerry had to sleep in it since Jack wouldn't let him stay over for the night because Jerry made a wisecrack about Jack's pen. By the end of the episode, Morty and Helen bought the Cadillac back from Jack.
A blog dedicated to the legality of the issues that arise in Seinfeld episodes, Seinfeld Law, has analyzed many of the classic Jack Klompus moments as they might have played out in a court of law.