After coming through the youth academy of Partizan, Živković made his senior debut with their affiliated side Teleoptik.
He was promoted back to Partizan in the winter of 2013, penning a four-year deal.
On 22 May 2013, Živković made his competitive debut for the club in a 2–0 away win against Smederevo.
He made two league appearances in the 2012–13 season, as the club won the national championship title.
On 24 January 2014, Živković signed a contract with Vojvodina until the summer of 2016.