Žaliukas was released by Hearts during the 2013 summer transfer window, after the club had entered administration. After leaving Hearts, Zaliukas joined Rangers on trial. Rangers offered Zaliukus a contract, but he rejected the contract offer from Rangers to pursue other options. After turning down a deal at Rangers, Žaliūkas joined Queens Park Rangers (QPR) on trial in the hope of earning a permanent contract, after impressing on trial Harry Redknapp confirmed that Žaliūkas would be an option to sign permanently, however with QPR still making a decision on a contract offer, Žaliūkas joined Leeds United on trial and QPR instead signed Oguchi Onyewu after losing out on Žaliūkas.