[2] Kalmár began his professional career with Nemzeti Bajnokság I club ETO Győr in 2013, winning the league title in his first year, before moving to 2.
He then moved on loans to FSV Frankfurt, Brøndby and DAC Dunajská Streda, agreeing to join the latter on a permanent deal in 2018, growing out to become team captain in his second season at the club.
He scored a goal in the season opener in the Szuperkupa against Debreceni VSC in a match won 3–0 at the Ferenc Puskás Stadium.
[8] He made his debut on 22 August, coming on as a substitute for Joshua Kimmich during a 1–0 home win against Erzgebirge Aue.
Fellow Hungarian Zsolt Korcsmár played for the guests, as Kalmár appeared for 25 minutes during the match and received a yellow card.
Two minutes later, his free kick was saved by opposing goalkeeper Daniel Haas, but managed to be decisive as Michael Parensen scored an own goal off Kalmár's pass.
[15] On 10 January 2016, during the winter break, he entered the pitch in the second half of the pre-season friendly against German sixth tier club FC Eilenburg and scored a hat-trick as Leipzig won the match 13–0.
[16] He finished the season with four league appearances, and due to a lack of playing opportunities, Leipzig wanted to send him on loan.
Fortuna Düsseldorf, FSV Frankfurt, Ferencváros and Sturm Graz were suitors in signing him on a loan deal.
[20] He finished his stint in Frankfurt with 12 league appearances, in which he scored the sole goal and contributed with one assist, before returning to Leipzig after his loan deal expired.
Kalmar inherited the number 11 jersey from Brøndby legend Johan Elmander, who had left the club in the summer of 2016.
In the pre-season friendly against South Korean club Jeonbuk Hyundai Motors he made his first appearance in the starting line-up, as they won 3–1.
[24] Four days later in the league against AC Horsens, Kalmár made as assist when he in the 16th minute curled the ball from a free kick which Rodolph Austin headed home.
[29][30][31] He made his debut for the club three days later in Fortuna Liga, on 13 August, in a match against Slovan Bratislava, replacing fellow countryman Kristopher Vida in the 55th minute.
[35] On 6 July 2018, DAC Dunajská Streda triggered the option to buy Kalmár from RB Leipzig, signing him on a three-year contract.
[39] On 2 October, in the fifth round of the Slovak Cup, he scored two goals and made an assist as DAC won 5–2 over third-tier club MFK Vranov nad Topľou.
[42] At the end of the season, he had scored eight goals in 29 league appearances together with five assists, as DAC finished as runners-up in Slovak Super Liga.