Altay Bayındır was born on 14 April 1998 in Bursa, Türkiye, and came through the academy ranks at Ankaragücü, making his top-flight debut for the club in a 1–1 draw with Çaykur Rizespor in November 2018. His performances caught the attention of one of Türkiye's biggest clubs, and in July 2019 he joined Fenerbahçe on a four-year deal, going on to make 145 appearances and establishing himself as their undisputed first-choice goalkeeper. During his time there he won the Turkish Cup in 2022–23, and his consistent shot-stopping earned him a reputation as one of the stronger keepers in the Süper Lig.
In September 2023, Bayındır made history by becoming the first Turkish player to sign for Manchester United, joining on a four-year deal for a reported fee of £4.3 million. He made an immediate impact in cup football, most notably in the FA Cup fifth-round tie against Arsenal in January 2025, where he saved a penalty from Martin Ødegaard in normal time and another from Kai Havertz in the subsequent shoot-out, earning Man of the Match honours. He had earlier collected an FA Cup winner's medal with United in 2023–24.
A calm and composed shot-stopper with reliable reflexes, Bayındır serves as a capable option between the posts for United, providing competition and cover in the squad. At international level, he made his senior debut for Türkiye in May 2021 and has been part of the national setup since, including a role at UEFA Euro 2024.