*Club domestic league appearances and goals, correct as of 06:42, 4 June 2024 (UTC) ‡ National team caps and goals, correct as of 23:24, 22 June 2024 (UTC)
On 8 July 2019, Bayındır joined Fenerbahçe on a four-year contract.[3] Bayındır became the first-choice goalkeeper ahead of teammate Harun Tekin.[4] On 19 August 2019, he made his Fenerbahçe debut in a 5–0 win against Gaziantep at Şükrü Saracoğlu Stadium.[5]
On 3 October 2020, Bayındır saved a penalty from Erik Sabo in a week 4 encounter against Fatih Karagümrük which ended 2–1 to Fenerbahçe.[6] On 6 December 2020, he saved another penalty, from Radosław Murawski, in a week 11 encounter against Denizlispor which Fenerbahçe won 2–0.[7] He produced total of seven saves during this game, in which Fenerbahçe were down to 10-men following the sending-off of Serdar Aziz.[8]
On 30 October 2021, in a 2–1 away defeat to Konyaspor, Bayındır was injured in a collision with Serdar Gürler in the 69th-minute and left the field, being replaced by Berke Özer.[9] The following day, Fenerbahçe made an announcement, saying: “Although no fracture was detected in Altay Bayındır’s shoulder, acromioclavicular separation was observed. It has been decided that our player will undergo surgery and his treatment has started.”[10] It was estimated that he would be unavailable for approximately three months.[11]
On 18 March 2023, Bayındır extended his contract, which was due to expire at the end of the season, until 2027.[12] On 17 April 2023, he had a lumbar hernia surgery.[13]
Manchester United
On 1 September 2023, Bayındır joined Premier League club Manchester United on an initial four-year deal, with an option to extend his contract for a further season, making him the first Turk to sign for the club.[14][15] The transfer fee was reported to be £4.3 million.[15] He made his debut on 28 January 2024 in a 4–2 away win against Newport County in the FA Cup, becoming the first Turkish player to feature for the club.[16]