You become capable with the Persuasion skill. If you are already capable, you become proficient. If you are already proficient, you gain expertise with it.
Additionally, you can add half your proficiency bonus (rounded down) to any Charisma check to calm violent emotions or to counsel peace that doesn’t already use your proficiency bonus. You must make this entreaty in good faith; it doesn’t apply if proficiency in the Deception skill applies to your check.