For recitals and chamber music, Ibragimova has appeared at venues including Wigmore Hall in London, Concertgebouw in Amsterdam, Mozarteum University of Salzburg, Musikverein in Vienna, Carnegie Hall in New York, the Palais des Beaux-Arts in Brussels. She has appeared at festivals including Salzburg, Verbier, MDR Musiksommer, Lockenhaus, Manchester International, and Aldeburgh. With her regular recital partner, Ibragimova performed the complete Beethoven violin sonatas at the Wigmore Hall London in 2009/10 (the recordings of which were released on the Wigmore Hall Live label). In 2015 she performed the six Bach Solo Sonatas and Partitas in the Royal Albert Hall as part of the Promenade Concerts.
In 2015 Ibragimova was married to Tom Service, a writer and classical music critic, whom she met when he interviewed her for The Guardian. They lived in Greenwich, London. The couple divorced in 2018.