Noor is the grandson of squash player Qamar Zaman.[3]
In 2022, he won in the boys under 19 categories at the Asian Junior Squash Championships.[4]
He was part of the men's team that won a silver medal at the 2022 Asian Games.[5] In the final against India, he played against Abhay Singh, and was defeated, winning two games out of five.[5] The team won the silver medal.
In 2024, Zaman won his 2nd PSA title after securing victory in the CAS Serena Hotels International during the 2024–25 PSA Squash Tour.[6]
In March 2025 he won the Liverpool Cricket Club Open (his 3rd PSA title) and a 15k PSA Challenger event, defeating Rory Stewart 3-0 in the final and one month later in April 2025, he beat K. El Torkey from Egypt to win the Under-23 World Squash Championships. In September 2025, he won his 4th PSA title after securing victory in the NASH Cup[7] and won a 5th (the CAS International) in November 2025, during the 2025–26 PSA Squash Tour.
