His father, at that time, looked down upon singing or learning to play a musical instrument as a profession for his boy, due to his family's origins as Dogras of Jammu.

Mian Kadir Bakhsh, who had no sons, formally adopted Alla Rakha and called him the next head of the Punjab gharana of tabla players (a 'gharana' is a community of musicians sharing a distinctive musical style).

[3][5][4][8] Alla Rakha also took vocal training in classical music and Raag Vidya under Ustad Ashiq Ali Khan of the Patiala gharana.

[9][4] Allah Rakha had a third daughter named Roohi Bano (1951–2019) who was born in Pakistan and achieved a "legendary" status in television and film acting in that country.

[7][10][11] Ustad Alla Rakha began his career as an accompanist in Lahore and then as an All India Radio, Delhi staffer in 1936 but later moved to Bombay in 1940, playing the station's first ever tabla solo and elevating the instrument's position in the process.

[4] Leading American percussionists in rock n' roll, such as the Grateful Dead's Mickey Hart, admired him and studied his technique, benefiting greatly even from single meetings.

Hart, a published authority on percussion in world music, said: "Allah Rakha is the Einstein, the Picasso; he is the highest form of rhythmic development on this planet."

[8] Qureshi died on 3 February 2000 at his Simla House residence on Nepean Sea Road following a heart attack, which he suffered on learning of the death of his daughter, Razia, the previous evening during cataract surgery.