Hajduk Beograd
After youth categories spent with Red Star Belgrade, Kljajić started his career in Hajduk Beograd. He made 8 appearances in Serbian First League, and was declared as a man of the match 3 times with average rating 7.31. Šumadija Jagnjilo
= 2009-2010 After playing for Hajduk Beograd, he left to Jagnjilo, and joined Šumadija for 2009-2010 season.
Kljajić played 28 times, with average rating 7.31, and also was declared as a man of the match 2 times.
= 2010-2011 He also played for Šumadija in first half of 2010-2011 season and made 13 appearances. Metalac Gornji Milanovac
= 2010-2011 Kljajić signed with Metalac for second half of season, and mainly was a reserve for Dejan Bogunović.
Interestingly, he was licensed with squad number 9, atypically for goalkeepers. He was in first 11 3 times.
= 2011-2012 On the beginning of season, Kljajić changed his jersey number, and took 12.
He shared his position with Živko Živković, but he was selected as a first choice in front of goal 17 times. He was also declared as the best on the field 3 times. Rad
= 2012-2013 After Metalac"s relegation from SuperLiga, Kljajić joined Rad.
Coach Nikolić included him in first 11 24 times in front of his competitors Branislav Danilović, Aleksandar Jovanović and Boris Radunović.
= 2013-2014 On 10 November 2013, Kljajić saved penalty kick from Dragan Mrđa. Foreign the first half of 2013-2014 season Kljajić made 14 appearances, and was declared as a man of the match 1 time.
After 2014, he received the contract termination on the detriment of the club Partizan
On 14 February 2014, Kljajić came to Partizan and signed a four-year contract with Partizan and took the number 12 on shirt.
= Loaning to Teleoptik After signing for Partizan, Kljajić was sent to Teleoptik, on loan.
He collected 12 games in second half of 2013-2014. = 2014-2015 Caoach Marko Nikolić, who also trained Kljajić in Rad included him in first 11 in a cup against Sloga Petrovac na Mlavi. He was in protocol several times, but made no league debut.
He has also been on the bench four times, in Union of European Football Associations Europa League, two times against Beşiktaş, one time against Tottenham Hotspur and Asteras Tripoli.
During the season he was not given a chance beside Milan Lukač and Živko Živković, mainly defended in friendly matches and several times was on the bench.