Vančura made his debut in the FIS Cup on February 21, 2015 in Hinterzarten and finished in 40th place. In the summer of 2015 he took part in other FIS Cup competitions, with his best result being 4th in Villach . He also started the Continental Cup for the first time on August 8th in Wisła . He finished in the top ten with the 7th place right at the first use. On August 29, he landed in the Czech Frenštát pod Radhoštěm for the first time on the podium of a Continental Cup jumping when he was third. Vančura then made his debut in the Grand Prix . On September 5 and 6, 2015, he competed at the Grand Prix in Tchaikovsky . But he only finished 36th and 46th and couldn't get any points. At further starts in the Continental Cup in summer 2015 and also in the following winter, he achieved further placements in the points ranks. On January 9 and 10, 2016, he was ninth and third in Garmisch-Partenkirchen . Because of these achievements, he was nominated for the Czech team at the 2016 Ski Flying World Championships in Bad Mitterndorf . In the individual he landed on rank 23 and with the team he was sixth. He then continued jumping in the Continental Cup, winning his first Continental Cup competition on January 22, 2016 in Sapporo . A week later he made his World Cup debut, also in Sapporo. In the first competition he finished 37th, on the second day he got his first World Cup points with 28th place. In February he took part in the Nordic Junior World Ski Championships 2016 in Râșnov . He was seventh in the individual, sixth in the team and fifth in the mixed team competition on the normal hill.
At the 2016 Grand Prix he achieved a total of four placements among the top ten, including his first podium finish in this series of competitions with second place in Tchaikovsky. In the overall standings, he finished twelfth. In the World Cup season 2016/17 he took part in the Four Hills Tournament for the first time . However, he could only qualify for the competition in Bischofshofen and finished the tour in 62nd place in the overall standings. On January 29, 2017, he won his second competition in the Continental Cup in Bischofshofen ahead of Simon Ammann and Clemens Aigner , after finishing second behind Aigner the day before. At the 2017 World Championships in Lahti , Finland , he was 35th on the normal and 42nd on the large hill. With the Czech team, he finished seventh.