Durante was born in Rome and started ballet there at the Teatro dell'Opera di Roma at six years old. Spotted by ballerina Galina Samsova at age ten, she joined the lower school of the Royal Ballet School at White Lodge in Richmond Park, London. A year later she was the subject of a Thames Television documentary entitled I really want to dance. In 1983 she graduated to the upper school, but within a year, aged 17, she was invited to join the Royal Ballet Company. At 19 she was promoted to soloist and at 21 she became a principal dancer. At the time she was the Royal Ballet's youngest principal, and a year later, in 1990, she became the youngest ever artist to receive the Evening Standard Ballet Award.
At the Royal Ballet, Durante danced all the main roles in ballets by Sir Kenneth MacMillan (Manon, Romeo and Juliet, Mayerling, Different Drummer, My Brother, My Sisters, Requiem, Elite Syncopations, Gloria, The Prince of the Pagodas and Anastasia, for which she was nominated for a Laurence Olivier Award), Sir Frederick Ashton (Cinderella, La fille mal gardée, Rhapsody, Ondine, A Month in the Country, A Midsummer Night's Dream, Symphonic Variations, Les Patineurs, Birthday Offering, Scènes de ballet, Thaïs pas de deux) and from the classical repertory (Swan Lake, The Nutcracker, Giselle, The Sleeping Beauty, La Bayadere, Don Quixote, Les Biches, Raymonda, Diana and Actaeon, Sylvia pas de deux).
She created roles in MacMillan's The Judas Tree and Winter Dreams (based on Anton Chekhov’s Three Sisters), in Wayne McGregor's Fleur de Peux, in Ashley Page's Pursuit, Piano, Bloodlines, ...now languorous, now wild... and Cheating, Lying, Stealing, in Will Tuckett's Present Histories, in David Bintley's Tombeaux and in Amedeo Amodio's Cabiria.
In 1992 Durante and her fellow principal Darcey Bussell were the subjects of a South Bank Show documentary Two Ballerinas at the Royal Ballet (UK: Two Royal Ballet Dancers), and the following year both were invited by the New York City Ballet for the Balanchine Celebration at the New York State Theater.
In 1995, she appeared in the title role of a ninety-minute version of Tchaikovsky's The Sleeping Beauty, which was telecast on Great Performances by PBS during the Christmas season. In 1998, Durante made a return to the Rome stage as a guest artist in Prokovsky's production of the Tchaikovsky ballet.