Meerits came through the Flora youth system. He moved to Esiliiga club Warrior on loan for the 2008 season. Meerits made his debut in the Meistriliiga on 15 May 2010, in a 2–1 win over Kuressaare. He made 10 appearances in the 2010 season as Flora won their eighth Meistriliiga title. In the Estonian Supercup on 1 March 2011, Meerits kept a clean sheet against Levadia for 120 minutes, eventually winning the match 5–3 in a penalty shootout by saving Konstantin Nahk's attempt and converting a penalty himself.[2]
Vitesse
On 7 July 2011, Meerits signed a three-year contract with Dutch Eredivisie club Vitesse.[3] He made his debut in the Eredivisie on 7 August 2011, when he came on as a 21st-minute substitute replacing the injured Eloy Room and kept a clean sheet in a 0–0 away draw against ADO Den Haag.[4]
Flora (loan)
On 25 February 2013, Meerits returned to Flora on a five-month loan until the end of July.[5]
FC Emmen
On 4 July 2014, Meerits signed a two-year contract with Dutch Eerste Divisie club FC Emmen.[6] In his first season with FC Emmen, he conceded 51 goals in 36 Eerste Divisie matches. In the 2015–16 season, Meerits was sidelined by a knee injury.[7]
Tarvas
On 30 August 2016, Meerits joined Meistriliiga club Tarvas until the end of the 2016 season.[8]
VPS
On 27 January 2017, Meerits joined Finnish Veikkausliiga club VPS on a one-year deal with an option to extend the contract for another year.[9] He made his debut in the Veikkausliiga on 5 April 2017, HJK.
Narva Trans
On 16 February 2019, Meerits signed a one-year contract with Meistriliiga club Narva Trans.[10] On 25 May 2019, he captained the team in a 2–1 extra-time victory over Nõmme Kalju in the Estonian Cup final.[11]
On 14 December 2010, Meerits was named by manager Tarmo Rüütli in the Estonia squad to face China PR and Qatar in friendly matches.[12] He made his senior debut for Estonia on 18 December 2010, replacing Pavel Londak in the 89th minute of a 0–3 away loss to China PR.[13]