This is a regular verb. It follows the conjugation pattern of the verb vivir.
PresentPresente
Carlos asume la responsabilidad del proyecto.
Carlos takes on responsibility for the project.
PreteritePretérito indefinido
La directora asumió su cargo en enero.
The director took up her post in January.
FutureFuturo
Este año asumiremos los costes del viaje.
This year we will assume the costs of the trip.