What is the ruling on obtaining a license through mediation after repeated failures, and what is the expiation for that?

It is not permissible to engage in an act of "wāsiṭah" (mediation/favoritism) because it is a form of deception. The one who commits an evil intercession (shafāʿah sayyiʾah) has a share in its sin. The door of repentance is open through seeking forgiveness (istighfār), regret, and a firm resolve not to return to it. And Allah forgives all sins.