[1][2] Internationally he has represented FR Yugoslavia (Serbia and Montenegro) and Spain, winning a World Championship bronze medal and one gold.

In 2002 he reached with Veszprém the EHF Champions League final, just to fell short against SC Magdeburg with an aggregate score of 48–51.

While playing for Ciudad Real (2004–2011) and its successor Atlético Madrid (2011–2012), he was named the best goalkeeper of the league five times in a row (2006–2010) and in 2006 he also got the Liga ASOBAL MVP Award.

[8] In 2012, after eight successful seasons in Ciudad Real and Atlético Madrid, Sterbik switched to league rivals FC Barcelona Handbol, having signed a four-year contract with the Catalan team.

In addition, with RK Vardar, in season 2014–2015, he managed to enter the quarter final of the EHF Champions League and to be part of the top 8 handball teams in Europe.

[11][12] Arpad's sister, Andrea Sterbik is also a professional handballer who plays for Hungarian top division club Kiskunhalas NKSE.