He was subsequently promoted to their first team in the spring of 2007, before signing his first professional contract with the club on 1 June 2007, on a five-year deal.
He made his competitive debut for the club in a 5–1 home league win over OFK Beograd, on 8 December 2007, coming on as a substitute for the injured Darko Božović.
[2] In the summer of 2008, in order to gain more playing time and experience, Živković was sent on loan to Metalac Gornji Milanovac.
In the following season, the club's first in the top flight, Živković missed only one out of 30 games, helping his team avoid relegation.
After leaving Gornji Milanovac for the second time, Živković started the 2012–13 campaign at Teleoptik, before being promoted back to Partizan in October 2012, as a replacement for the injured Vladimir Stojković.
In the following season, Živković made his debut in UEFA competitions, coming on as a substitute for the injured Milan Lukač in the second leg of the Champions League third qualifying round versus Ludogorets Razgrad on 6 August 2013.
On 21 April 2019, the Serbian goalkeeper announced via his facebook account his decision to leave the club, upon the expiration of his contract.
Živković represented Serbia and Montenegro at the 2006 UEFA Under-17 Championship, together with his club teammates Stevan Jovetić and Nikola Gulan, among others.