[1] Pospěch started his career with hometown side Opava, where he spent five years before later playing top-flight football for Slovácko and Slovan Liberec.
[2] In November 2009, the Czech Disciplinary Commission suspended Pospěch, which left him unable to play professional football until October 2010.
[4] Pospěch missed almost two years of league football before scoring on his return to action in a 1–0 win for Slavia Prague against former club Slovan Liberec in March 2011.
[8] After signing for Dukla Prague in the summer of 2012, Pospěch took until October 2012 to score his first league goal for the club, which came in a 1–0 win against Hradec Králové.
Pospěch scored four goals in a match, becoming just the fifth player in the history of the Czech league to do so, in July 2013 during Dukla's 4–0 win against Sigma Olomouc.