Her first collection, Espuma (Foam) was published three years later, and two of its short stories were made into TV scripts for Cuban television.
In 2010, this novel was adapted for the stage in France and, in 2013, the University choral ensemble of Montpellier, Ecume, created "Cubana soy", a creation for the musical theatre.
In 2007, the Hay Festival and the organizers of the Bogotá World Book Capital selected Karla Suárez as part of the Bogotá39 for the most promising Latin American writers under the age of 39.
She earned scholarships in Cuba (Razón de Ser) and France (Centre national du livre, Paris) Maison des Ecrivains Etrangers et Traducteurs, Saint-Nazaire; Agence Régionale pour l'Écrit et le Livre en Aquitanie, Bordeaux; and Clermont Communauté, Clermont-Ferrand.
She coordinates the Reading Club of Lisbon at El Instituto Cervantes and she is also Professor of Creative Writing at the Escuela de Escritores in Madrid.