Raised in the Stockholm suburb Jordbro, Jajić started his career at local club IFK Haninge/Brandbergen where he made his senior debut in 2013 at age fifteen.
[5] He would make another 3 appearances in Allsvenskan for Hammarby during the 2016 season, whilst also enjoying a short loan stint to their affiliated club Enskede IK in the Swedish third tier.
[8] Midway through the season, on 21 July 2017, after only appearing in 3 league games, Jajić went out on a six-month loan to IK Frej in Superettan.
[9] Jajić also spent the vast majority of the 2018 season on loan at IK Frej, scoring 9 goals in 29 league appearances in the Swedish second tier.
[16] Jajić captained his country during the 2017 UEFA European Under-19 Championship, where Sweden finished last in its group following two losses in even games against Czech Republic and Georgia, and a surprising 2–2 draw against Portugal.