In October 2014, Veenstra won the Luxembourg Open beating Mark Oosterhuis in the Final 6–4.[2] He reached the semi-finals of the 2015 Denmark Masters and England Open.[3][4] In October 2015, he won WDF World Cup Pairs with Wesley Harms to beat Scott Mitchell and Mark McGeeney 6–3.[5] On his debut at the 2016 BDO World Darts Championship, Veenstra caused an upset beating compatriot and third seed Jeffrey de Graaf 3–2 in the first round, before beating English player Martin Atkins comfortably 4–0 in the second round. Veenstra then defeated defending champion Scott Mitchell 5–3 to reach the semi-finals, which he narrowly lost to Jeff Smith 6–5.
At 2023 European Q-School, Veenstra secured a PDC tour card for the 2023 and 2024 seasons by finishing second on the European Q-School Order of Merit.[6]