Morte made his feature film debut when he played the minor role of Rafael Torres in the Spanish film Lola, la película (2007). But, he had his first main role in feature film when he played the role of David Ortiz in the Netflix Spanish film Mirage (2018). In 2019, he played the role of Óscar in the Movistar+ Spanish television series El embarcadero.
In December 2019, Morté was announced to have joined the cast of the Amazon tv-series Wheel of Time, an adaption of the epic fantasy novels of the same name. Morté is set to portray Logain Ablar.
