Sabit Abdusalam would play for Xinjiang Youth and was part of the team that qualified for the first round of the 2013 Chinese FA Cup and made his first senior appearance in the team that on 30 March 2016 beat Jiaozhou Fengfa 2–1.[1] He would go on to join second-tier club Xinjiang Tianshan Leopard and make his debut in 2015 Chinese FA Cup game on 19 August 2015 against Jiangsu Guoxin-Sainty in a 3–1 defeat.[2] He would gradually start to establish himself as a regular within the team and go on to score his first goal for the club in a league game on 12 March 2016 against Shenzhen in a 2–1 defeat.[3]
On 3 April 2021, Sabit Abdusalam left Xinjiang Tianshan Leopard after making over a hundred appearances for them to join top-tier club Cangzhou Mighty Lions.[4] He would make his debut in a league game on 14 May 2021 against Guangzhou City in a 0–0 draw.[5] This would be followed by his first goal for the club, which was in a league game on 21 December 2021 against Tianjin Jinmen Tiger in a 2–1 victory.[6]
On 30 March 2022, Sabit would join fellow top-tier club Changchun Yatai on a free transfer for the start of the 2022 Chinese Super League season.[7] He would make his debut for Changchun in a league game on 15 April 2023 against Zhejiang Professional in a 2–0 victory.[8]