Puy Navarro began her career in Spain, acting in classical plays. She has performed internationally in Spain, Japan, Cuba, and the US. She’s worked with renowned directors such as Stephen Daldry, Luis García Berlanga, and Jorge Alí Triana. Puy has played with many New York-based theater companies doing classical, experimental theater and clown. Recent independent film and TV credits include, Men Who Build America, Stray Dolls (Tribeca Film Festival), He Matado a Mi Marido, and Love Comes Later (Cannes Film Festival–Semaine de la Critique).

Puy began writing when she felt the need to turn her play Life is a Dream, or the Crime of Being Born. into a film script inspired by the Desaparecidos in Argentina’s Dirty War. Her research for the play was conducted in Buenos Aires in collaboration with Fernando Castets and Aída Bortnik. The script was developed at Dreamago’s Writer’s Lab in Switzerland under the supervision of Christopher Hampton. Her theater play Else and Henry was awarded the third prize in the Metlife Foundation’s national writers’ competition "Our Voices." In 2019, she won a film pitch contest and an Artis Residency in Switzerland, to turn Else and Henry into a film script.