At the age of just 15 he was called up to play for Dinamo's senior team, alongside fellow midfield legends such as Ilir Përnaska, Shyqyri Ballgjini and Muhedin Targaj.
Demollari played his entire career in Albania for Dinamo Tirana, alongside fellow internationals Genc Ibro, Eduard Abazi and Agim Canaj, winning two league titles.
[4][6][7] Demollari made his Divizia A debut on 25 August 1991 in a 6–0 victory against Petrolul Ploiești in which he scored two goals and gave an assist, being nicknamed "Dobrin of Albania" by the Gazeta Sporturilor newspaper.
[8][13] He played a total of 25 games, scoring three goals in European competitions, including appearing in Dinamo București's 2–1 victory on aggregate against Luis Figo's Sporting Lisabona in the 1991–92 UEFA Cup.
[6][11][13] Sulejman Demollari was part of Albania U21's generation that finished the qualification group on the 1st position in front of West Germany U21 at the 1984 UEFA European Under-21 Championship where in the quarter-finals they were eliminated by Italy U21 after a double 1–0 loss.