|2004 Athens||Team Competition|
|World Men's Handball Championship|
|2003 Portugal||Team Competition|
|2005 Tunisia||Team Competition|
|2009 Croatia||Team Competition|
|2001 Tunis||Team Competition|
Šprem started his professional career with RK Zagreb in the late 1990s. He also spent a season with RK Medveščak Zagreb in 2001 and 2002, before returning to RK Zagreb for a second spell with the club between 2002 and 2004. He eventually left RK Zagreb for German side SG Flensburg-Handewitt in October 2004. He left Flensburg for a short spell with TuS Nettelstedt in February 2005, returning to the club in the summer of the same year and eventually spending a season with them. In the summer of 2006, he left Flensburg for a short spell with MT Melsungen, before joining his current club, HSG Nordhorn, in November 2006. He left Nordhorn in 2009.
Šprem is also a member of the Croatian national handball team, with whom he won gold medals at the 2003 World Men's Handball Championship and the 2004 Summer Olympics. He also won two silver medals with the Croatian national team at the World Men's Handball Championships in 2005 and 2009, and participated at the 2006 European Men's Handball Championship, where Croatia finished fourth.
- "2004 Summer Olympics – Athens, Greece – Handball" databaseOlympics.com (Retrieved on February 1, 2008)
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