 Žaliūkas made his Leeds debut against Yeovil Town on 1 November 2013, Žaliūkas rescued a point for Leeds in a 3–3 draw against Watford on 7 December by blocking a goal bound effort in the last minute of the game.Žaliūkas' impressive performances during the absence of injured defender Scott Wootton meant Žaliūkas became one of the first names on the teamsheet under Leeds manager Brian McDermott as part of three centre backs with Tom Lees and Jason Pearce in Leeds' 3–5–2 formation.In December 2013, Žaliūkas was victim of straight red card challenges in successive games, first Marcus Tudgay was sent off for Barnsley on 21 December for a challenge on Žaliūkas, and then Kirk Broadfoot for Blackpool on 26 December was also sent off for a bad challenge on Žaliūkas.