He spent seven years there, playing 193 games and scoring 13 goals, and captaining the team to win the Scottish Cup in 2012.

[4] Žaliūkas made his competitive debut on 26 August in a 4–1 victory over Inverness Caledonian Thistle,[5] and scored his first goal for the Tynecastle club to secure a 2–2 draw at St Mirren on 2 December.

[7] Further to his impressive start to the 2008–09 season, it was reported by BBC Sport that major clubs in Moscow were willing to sign the defender.

[10] In July 2009, following the departures of captain Robbie Neilson and vice-captain Christos Karipidis to Leicester City and AC Omonia respectively, László named Žaliūkas as one of the candidates to take the club captaincy, along with midfielders Michael Stewart and Laryea Kingston.

[13] Soon afterwards, however, Žaliūkas' future at Hearts was put in doubt due to failed contract negotiations, which resulted in him being left out of the team.

However, when the club delayed a possible contract offer, Žaliūkas joined Leeds United on trial and QPR instead signed Oguchi Onyewu.

[18][19][20] In October 2013, Žaliūkas began training with Leeds United for a trial spell, the club picking him for a development squad match, amid rumours that they would offer a contract.

[28] On 31 December 2013, Žaliūkas' impressive form was rewarded when he signed an extended and improved contract at Leeds until the end of the 2014–15 season.

[29] However, after a series of individual mistakes in the 6–0 defeat against Sheffield Wednesday, Žaliūkas lost his place in the Leeds United team.

[38] According to Lithuanian Football Federation president Tomas Danilevičius, Žaliūkas was diagnosed with motor neurone disease in 2013.

[36] Hearts retired the number 26 jersey in Žaliūkas's honour for 2021–22, while making MND Scotland their sponsor for two years.