Career
Born in Titograd, Kljajević began playing football with the youth side of FK Bokelj. He played for FK Zeta, before joining Greek Superleague side Panachaiki F.C. in July 2002. He would next play for fellow Superleague club Egaleo F.C., before moving to Serbian FK Rad Belgrade and already back in Montenegro, FK Grbalj.
Since the winter-break of the 2009-2010 season, he has been playing with FK Kom.