Her operatic début was at the age of 16 in Malta as Amina in La Sonnambula, followed by engagements in Naples, Genoa, Rome, Florence, Madrid, and Lisbon. She sang at the Lyceum Theatre, London for the 1857 season (the year after the Royal Opera House in Covent Garden burnt down), and between 1859 and 1865 appeared in opera at both Covent Garden and Her Majesty's Theatre. During this time, she participated in two operatic premieres, creating the title role in Alfred Mellon's Victorine on 19 December 1859, and the role of Mabel in MacFarren's opera Helvellyn on 5 November 1864. She sang with Charles Santley at the opening of the Oxford Music Hall in 1861. She also was a successful oratorio and concert soloist, in constant demand in Britain, and she participated in the 19th-century English revival of the music of George Frideric Handel.
Her first husband, Army Captain H. de Wolfe Carvelle, died in 1865, sixteen months after their marriage. In 1866, she appeared before the Royal Philharmonic Society in Robert Schumann's Paradise and the Peri. She then toured the United States with cornetist Levy and violinist Carl Rosa, the latter of whom she married in New York City in 1867. Together they quickly established the Parepa-Rosa English Opera Company there, which became popular, and which introduced opera to places in America that had never staged it before. They opened at the French Theatre on Fourteenth Street, New York City in September 1869 with a performance of Bale's opera The Puritan's Daughter, with Parepa singing the title role. The subsequent tour of the eastern and midwestern states included a repertoire that ranged from The Bohemian Girl and Maritana to Weber's Der Freischutz and Oberon.
In 1870, The Parepa-Rosa Opera Company returned to Britain and then appeared in Italian opera at Cairo, Egypt, followed by a return to America for another successful tour in 1871-71. In 1872, they returned to Britain. In September 1873, the company changed its name to Carl Rosa's English Opera, since Parepa was pregnant.
Parepa-Rosa died in childbirth in London at the age of 37 while preparing a production of an English version of Richard Wagner's Lohengrin. Carl Rosa endowed the Parepa-Rosa Scholarship at the Royal Academy of Music in her memory.
William Winter wrote that "Great vocal powers have seldom found such ample or such touching expression as those of Parepa-Rosa did in the first act of Norma. ...one of her best successes was made as Rosina in The Barber of Seville... to indicate the versatility of her talents and the scope and thoroughness of her culture. Rosenthal comments in his 1980 Grove article that her range extended over two and a half octaves to d'', and that she was considered more successful in the field of oratorio than opera.