[1] After his graduation, Kobborg joined the Royal Danish Ballet and was promoted to the rank of principal dancer in 1994, following his debut in the role of James in La Sylphide.

Despite media speculation that Kobborg would retire from the stage to replace Dame Monica Mason as Artistic Director of the Royal Ballet in 2012, it was later announced that Kevin O'Hare would be her successor.

[8] Kobborg's Romeo & Juliet, premiered in the Arena di Verona on 26 August 2019 and attended by more than 10,000 members of the audience from all over the world was considered a great success.

Kobborg's performance as Albrecht in Giselle, alongside Alina Cojocaru as the title role was recorded in 2006 and aired in England on Boxing Day.

[citation needed] He choreographed the dance scene in the film The White Crow (2018),[14] a Rudolf Nureyev biopic directed by Ralph Fiennes.