What is happening here is that Paul is acting in lieu of the elders of the church at Corinth. He is doing what the elders should have done, and have failed to do, as though he were there.
There are no apostles today. No one should try to imitate the apostle today in giving instruction from afar to a local church to which they do not belong. The churches now must do this for themselves. Every autonomous individual congregation through its elders, its pastor, its officers, should initiate, inaugurate a process of discipline, based on the apostolic instruction in the word of God.