Acquired into the Ajax Youth Academy from local amateur side Amsterdamsche FC in 2007, Van der Hart worked his way up the youth ranks, and had an outstanding 2011–12 season with the Ajax A1 youth squad. That year, the under-20 team where he was first-choice keeper at the time, had won the national title, as well as finished as runners-up in that season's NextGen Series when they lost to Inter Milan on penalties. Van der Hart was awarded his first professional contract when he was pronounced as the first team's third-choice goalkeeper, as well as receiving the award for Talent van De Toekomst. His first contract was a three-year deal, binding him to the club until June 2015. The 2012–13 season was Van der Hart's first with the Ajax first team since the departure of former third keeper Jeroen Verhoeven, however with then first- and second-choice keepers Kenneth Vermeer and Jasper Cillessen each having an injury-free season, Van der Hart was unable to make his debut for the first team, meanwhile still playing in the Ajax A1 youth squad, where he was still eligible to participate due to his young age. On 8 April 2013, an opportunity presented itself for Van der Hart to appear as second choice keeper behind Jasper Cillessen, following a red card suspension to Kenneth Vermeer. That void would however be filled by Chiel Kramer, first keeper of the reserves team Jong Ajax, since Van der Hart was sidelined due to a groin injury at the time. Ajax would eventually go on to win the national title in what would be Van der Hart's first season as a professional. The 2013–14 season saw Van der Hart maintain his position as Frank de Boer's third choice behind Kenneth Vermeer and Jasper Cillessen, as the season opened with Ajax winning the Dutch Super Cup. Van der Hart made his professional debut on 9 August 2013 in the Eerste Divisie keeping for Jong Ajax, where he is still eligible to play, having made less than 15 appearances for Ajax first team in the Eredivisie. The match against Oss in which he played the full 90 minutes ended in a 2–0 loss for the Amsterdammers, in what would be only Jong Ajax second match ever in professional football, with the team having moved up from the Beloften Eredivisie before the start of the season.
On 9 June 2014, it was announced that Van der Hart would serve a season-long loan spell with Go Ahead Eagles in Deventer, joining the likes of Nick de Bondt and Sven Nieuwpoort who had transferred to the club from Ajax during the same transfer window as well.
On 14 August 2015, it was announced that Van der Hart had been sold to Eredivisie side Zwolle. He signed a one year-deal with the club, an extension option included.
Lech Poznań
On 21 May 2019 he signed a three-year contract with Polish side Lech Poznań. He made his debut in Lech on 20 July 2019 in a game against defending champion Piast Gliwice.
International career
Van der Hart has represented Netherlands U-18 and Netherlands U-19. On 11 November 2011, Van der Hart made his debut for Netherlands U-18 in a friendly encounter against Romania U-18. On 7 September 2012, Van der Hart made his debut for the under-19 team in a friendly match against Greece U-19. He was selected by head coach Wim van Zwam to participate in the 2013 UEFA European Under-19 Football Championship in Lithuania. Van der Hart played in all the group matches, of which 1 was won, and 2 were lost, failing to advance past the group stage. On 2 August 2013, head coach of the Netherlands U-21 team Albert Stuivenberg selected Van der Hart for the 32-man provisional squad, ahead of the 2013 UEFA European Under-21 Football Championship. On 9 August 2013, however, it was announced that Van der Hart had not made the final 22-man squad selection for the tournament.
