This is a regular verb with a spelling change. It follows the conjugation pattern of the verb vivir.
Spelling Change: go jo - ga ja - gá já
PresentPresente
Exijo una explicación.
I demand an explanation.
PreteritePretérito indefinido
El cliente exigió un reembolso.
The customer demanded a refund.
Present SubjunctivePresente de subjuntivo
No creo que el trabajo exija experiencia.
I don't think the job requires experience.