In the film, Jarda enters his home and secretly alerts the CIA Special Activities Division of Jason Bourne's whereabouts. He then enters his kitchen, opens his fridge and swivels around with a Beretta 92fs in hand and points it at Jason Bourne until he's notified that it's been emptied. Jason then restrains his hands and starts interrogating him about the current state of Treadstone. Jarda replies that the Operation was abandoned, the night he walked out and that Conklin was executed on the same night. Jarda then mockingly remarks "We're the last two." Bourne realizes that Jarda has sent for the CIA and asks for an escape route. Suddenly Jarda rises up from his chair, knocking Bourne off balance and making him drop his Sig P225 and grabs a carving knife in an attempt to get out of his restraints and kill Bourne. Bourne, however, rolls up a magazine and whacks Jarda in the face several times making Jarda lose the knife. Soon, they're both on the floor with Jarda trying to strangle Bourne with an electric power cord. Bourne, however, punches him twice in the face and starts to successfully garrote Jarda. Jason then sets up a surprise explosion for the backup team and leaves. The explosion then takes out the front of Jarda's house, injuring the armed operatives in a shower of bricks and alerting the police.
It is unclear how Bourne found out about Jarda's whereabouts or even remembered him in the first place. In their brief dialogue, it is hinted that Jarda did not bother to hide after he learned of Bourne's amnesia and the killing of every other Treadstone asset.
Jarda: "Word in the ether was you'd lost your memory."
Jason Bourne: "You still should have moved."
Since Bourne regained some of his memories due to the flashbacks during the 2 years following the events of The Bourne Identity, one explanation is that he remembered Jarda from earlier missions or training.
This is however unlikely, as Treadstone assets always operate on their own and e.g. the Professor does not seem to know Bourne on their encounter, asking in which city Bourne was stationed.
Another explanation is that Bourne acquired at least some intel about Treadstone and the whereabouts of the other remaining assassin when he briefly had access to the Treadstone hideout in Paris at the end of The Bourne Identity.
Curiously, Jarda and The Asset are two villains who attempt to strangle Jason Bourne during the fights.