Shortly after his birth, his father was appointed trade attaché to the Polish consulate in Bombay, and together with his older sister he learned to swim there.

Klim was first selected to represent Australia in the 1994 Commonwealth Games in Victoria, British Columbia, Canada, while still a student at Wesley College, Melbourne.

He rebounded to qualify for a finals in the 100m butterfly, and swam the freestyle leg in the 4×100 m medley relay, in which Australia claimed a bronze medal.

In January, the World Aquatics Championships were held in Perth, Western Australia, and in front of a boisterous home crowd, he was the leading swimmer of the meet.

His 100m freestyle world record bested by Pieter van den Hoogenband in the semi's, in the final he finished with a bitter 4th place, he turned first at the wall but he claimed his legs gave away in the second half.

Klim failed to qualify for the 2004 Athens Olympics, but was later selected as part of the relay team, which came second behind USA in the 4×200m, race.

In 2005, Klim swam at the World Aquatics in Montreal, returning to individual action, but failed to progress to the finals in the 50m & 100m Freestyle.

[6] Klim shares custody of his children with his ex-wife and continues to live in Bali with his current partner Michelle Owen.

[9] In July 2022, Klim revealed that he had been diagnosed with the auto-immune disorder chronic inflammatory demyelinating polyneuropathy in 2020, which has affected his legs and feet and left him struggling to walk unassisted.