Due to political circumstances, he was forced to complete the remainder of his studies in Albania.

[2] During the Kosovo War, he was appointed commander of the Counter Intelligence Service (G-2) of the KLA.

In the October 6th 2019 election, Veseli was the PDK's nominee for the prime ministership of Kosovo.

The indictment charged Veseli, Hashim Thaçi, and others for crimes against humanity and war crimes, including murder, enforced disappearance of persons, persecution, and torture, allegedly occurring during the 1998-99 Kosovo War.

[7][8] The defendants were charged with approximately 100 murders of Kosovo Albanians, Serbs, Roma, and political opponents.

[8] Veseli voluntarily surrendered to the tribunal after he was charged, claiming that he saw the trial as "an opportunity to finally answer the false allegations and rumours that have been circulating for many years".