Klaasen started his football career at the age of six at Zeeburgia.[2] He left the club after a year for Ajax's youth academy.[2] After playing in Amsterdam for five years, he moved to the youth academy of HFC Haarlem. There he played one year in the academy before moving to Feyenoord in 2006.[2][3]
He then joined AZ from Feyenoord's youth academy in 2007, and signed a two-year senior contract with the club on 19 May 2011.[2] Coming through the AZ academy, Klaasen described himself as a "holding midfielder, with a good shot and vision. I can be compared to Stijn Schaars."[4] Ahead of the 2012–13 season, some of the club's talents, including Klaasen, were given the chance to join the first team's pre-season friendlies. He would, however, play the season with the youth team. At the end of the season, Klaasen's contract was terminated.[5]
Kortrijk
Prior to the start of the 2013–14 season, Klaassen trialled with Kortrijk.[6] He tested for around four weeks before it was announced that he became part of the team, signing a three-year contract on 20 July 2013.[7] Klaasen made his professional debut on 27 July 2013, replacing Gertjan De Mets in the 78th minute of a 1–0 home win over OH Leuven.[8] On 7 December 2013, four months after his last appearance, he scored his first goal in professional football, the 1–1 equalizer in the 87th minute against Sporting Charleroi.[9][10] He made his first start on 22 February 2014, playing the full ninety minutes against Mons.[11]
Sparta Rotterdam
On 8 January 2016, Klaasen moved to Sparta Rotterdam, where he signed a contract until the end of the season with an option to extend for two seasons.[12] He made his debut for the club ten days later, on 18 January, replacing Ryan Sanusi in the 83rd minute of a 5–2 victory over RKC Waalwijk in the Eerste Divisie.[13] His first start came in the 2–1 league win at FC Den Bosch on 31 January.[14][15] On 12 February, Klaasen scored his first goal for Sparta in a 3–0 away win over Achilles '29.[16] Sparta picked up the option in Klaasen's contract on 22 February, extending his contract until 2018.[17]
Klaasen made five appearances for Sparta that, scoring once,[18] as the club won the Eerste Divisie and reached promotion to the Eredivisie.[19]
De Graafschap
On 26 January 2017, Klaasen was sent on a six-month loan until the end of the season to De Graafschap, competing in the Eerste Divisie.[20] He made his debut for the club as a starter in a 3–2 league loss to Jong FC Utrecht on 30 January 2017.[21] He signed a permanent deal with the club on 2 May 2017, a one-year contract with an option for an additional season.[22]
On 11 May 2018, Klaasen extended his contract with De Graafschap until 2019. Upon signing, technical director Peter Hofstede stated: "Robert has made strides this season. We think he can grow further and want to give him that chance here."[23]
Roda JC
On 7 July 2019, Klaasen joined Eerste Divisie club Roda JC on a two-year contract.[24] He made his debut for the club on the first matchday of the season as a starter in the 1–1 home draw against Almere City.[25][26]
Klaasen scored his first goal for Roda JC on 5 December 2020, opening the score from a free kick in a 1–1 draw away against Jong PSV.[27]
VVV-Venlo
Klaasen moved to VVV-Venlo on 10 June 2022, signing a two-year contract.[28] His club debut came on the first matchday of the 2022–23 season in a 3–0 home win over Almere City.[29] On 11 December, he scored his first goal for the club, helping the club to a 2–1 victory against provincial rivals MVV Maastricht.[30]
MVV
On 2 January 2025, Klaasen signed a contract with Eerste Divisie club MVV until June 2025, ending six months as a free agent.[31]
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