A formal apology was an official non-verbal or written apology granted to a wronged party on behalf of all those who committed wrongs.
Kai Winn Adami and Vedek Bareil Antos of Bajor attempted to open talks with Legate Turrel of Cardassia with the intention of establishing a treaty and to a final peace settlement between the two parties in 2371. Key talking points of the talks ranged "from war reparations to the exchange of ambassadors", and even included "the possibility that the Cardassians will issue a formal apology for the pain and suffering inflicted on the Bajoran people during the occupation." The result of these talks was the Bajoran-Cardassian Treaty. (DS9: "Life Support")