This is a regular verb. It follows the conjugation pattern of the verb vivir.
PresentPresente
Ese restaurante ya no existe en mi barrio.
That restaurant no longer exists in my neighborhood.
ImperfectPretérito imperfecto
Hace años existían muchas tiendas pequeñas aquí.
Years ago there were many small shops here.
FutureFuturo
En el futuro existirán coches sin conductor.
In the future there will be cars without drivers.