Veger made his ATP main draw debut at the 2013 PBZ Zagreb Indoors where he came through qualifying defeating Simon Greul, Kamil Čapkovič and Ante Pavić.

As a singles player, Veger reached a career high of 478 in February 2015.

[1] He had some success as a junior, reaching a highest ranking of 52 in singles and was also a finalist in the 2012 Australian Open Boys' Doubles alongside Adam Pavlásek, losing to the British pair of Liam Broady and Joshua Ward-Hibbert.

[2][3] Veger studied at Durham University from 2017 to 2018, also playing for and coaching the men's tennis team.

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