In 2007, she made her acting debut in the Antena 3 series The Boarding School, playing Julia Medina (Spanish: El internado). She would continue to feature in the series until its conclusion in 2010, earning a Fotogramas de Plata Award for Best Actress and a Golden Nymph award for Best Actress – Drama at the Monte-Carlo Television Festival in 2009.
Suárez made her film debut with Mario Casas in Neon Flesh (Carne de neón) in 2010. In 2011, the film was finally released. Suárez then featured in Pedro Almodóvar's The Skin I Live In, alongside Antonio Banderas and Elena Anaya, for which she received critical praise and a nomination for a Goya Award for Best New Actress.