The first few years as a player played Pešić in his hometown Rijeka in RK Zamet and with production license in Croatian second division club RK Senj. He then played for the Hungarian club MKB Veszprém KC, with which he won in the 2008/09 season, league and cup, as well as the Croatian first division club RK Zagreb, with whom he won three times the double. In 2012 he joined the Slovenian club RK Maribor Branik . After one season, he signed with the Belarusian club HC Meshkov Brest, with whom he again champion and cup winner was, 2014.
At a dance hall in February 2009 some Hungarian-Romani people attacked Pešić and teammate Marian Cozma with a knife. Pešić was so badly injured by a knife that he had to remove a kidney.[2] His teammate Marian Cozma died after two stab wounds to the heart, another colleague, Žarko Šešum, suffered skull fractures due to heavy kicks to the head.[3]
