His great season at Sparta had raised his profile, and not only did he break into the national team but a number of foreign clubs became interested in signing the promising young striker.

In the end he moved to Turkish team Trabzonspor in 2005 for a €3.25 million transfer fee, signing a five-year deal with the Süper Lig outfit.

The excitement of his transfer was short-lived, however, as he failed to make an impact, moving to Beşiktaş J.K. on loan after only a few months without having scored a single goal for Trabzonspor.

He was called back to Trabzonspor main squad for 2007/08 season by trainer Ziya Dogan after the loss of explosive striker Ersen Martin to injury, but did not feature.

In January 2009 he left FK Teplice on a six-month loan move to Austrian Bundesliga side SCR Altach.

With the expected pause for an injury like this no less than six months, Jun surprised everyone by making a speedy recovery, already being fit for a short comeback against Red Bull Salzburg on 21 March 2010.

He went on to score four times until the end of the 2009–10 season, making him second-best goal-scorer after Milenko Ačimovič with a total of nine goals and ten assists.

As well as his incomplete pre-season, Jun sustained a further serious injury in training in October 2010, a ruptured ligament in his ankle keeping him on the sidelines for another six weeks.

He struggled to make even substitute appearances at Beşiktaş, which has led to his omission from the Czech Republic squad for the 2006 World Cup.