This is a regular verb. It follows the conjugation pattern of the verb vivir.
PresentPresente
Mi abuelo insiste en pagar la cena.
My grandfather insists on paying for dinner.
PreteritePretérito indefinido
Pedro insistió en acompañarnos al aeropuerto.
Pedro insisted on coming with us to the airport.
Present SubjunctivePresente de subjuntivo
Aunque insistas, la tienda está cerrada hoy.
Even if you insist, the store is closed today.