Živković was a vital member of the Serbia national under-20 team that won the 2015 FIFA U-20 World Cup, scoring two goals and providing two assists.

[4] Živković made his competitive debut for their first team in a league fixture against Novi Pazar on 28 April 2013, replacing Darko Brašanac after 65 minutes of the match that ended in a goalless draw.

He entered the field as a 60th-minute substitute for Aboubakar Oumarou, managing to earn a free kick in the 81st minute, which would eventually result in the game-winning goal.

[13] On 17 September, Živković scored a goal and provided an assist in a 3–2 home victory over AZ in the opening round of the Europa League group stage.

The 24-year-old Serbian international was previously released by Benfica as part of their summer overhaul and PAOK snapped him up on a two-year contract for an undisclosed fee.

[22] Among some other highlights, on 29 April 2021, helped his club to seal qualification to the Greek Cup final with a spectacular lob in extra time, forming a 2–1 home win game against rivals AEK Athens.

[23] Zivkovic won the Greek Cup, his first trophy with PAOK, after helping his team win the final against Olympiacos with 1–2, giving a high class assist to one of his teammates on the 90th minute.

[24] On 9 December, he opened the score with a header, in a 2–0 UEFA Europa Conference League home win game against Lincoln, sealing the qualification of the club in the phase of Knockout round play-offs, for the first time in the last five years.

[25] PAOK footballers, on the wings of Andrija Živković, outclassed Hajduk Split with 3–0 in the Hell of Toumba Stadium and passed to the qualifying Play-off round of the 2023–24 UEFA Europa Conference League.

[26] On 20 August 2023 Andrija Živković confirmed that he is in "life form", PAOK defeated Asteras Tripolis 3–0 in the first round of the Greek championship, as he scored two goals tonight.

[27] On 15 May 2024, in a 4–1 victory over Panathinaikos, Živković once again proved that he is a key player when it matters most, stepping on the field in the 66th minute as a substitute for Taison, scoring two goals and assisting one.

[28] On 19 May 2024 PAOK achieved a great success by winning the title of Greek champion in the last round of the 2023–24 Super League Greece, defeating arch-rival Aris with a score of 2–1.

[29] Živković was a key member of the Serbia national under-17 team in two UEFA European Under-17 Championship qualification cycles,[30] but failed to help them reach the final tournament on both occasions.

On 11 October 2013, Živković became the youngest player ever to debut for Serbia, aged 17, after coming on as a substitute for Zoran Tošić in a 2–0 home friendly win over Japan.