If the report is true, Timothy must bring the sin of the elder to the whole church. Paul is eager that the sins of elders are not hidden, but dealt with publicly. The reason for this was that it would be a warning to the other elders so that they and the members would be more careful not to sin, being afraid of such public shame.
These things are very important, and Timothy must do what is right. Paul’s warning is very serious, saying that God, the Lord Jesus and the angels are there to see that Timothy does obey. There might be a case where two or three people would accuse an elder. Then Timothy must look at the facts, not act on his own opinions but search for what is true. Certainly, he must not act from prejudice.
To appoint a new elder, Timothy and the elders would put their hands on him, as they would do appointing people to any office or task in the church. To lay hands on them shows that they have the authority, and approval, to do the task. Paul tells Timothy not to be too quick in laying hands on anyone. He ought first to be sure that the person is fit for the office, and he needs to see that the person has the right qualities, and is ready for the task.
Those who lay their hands on a person are to some extent responsible for him and for what he does. If a bad choice has been made, they share in the faults of that person and share the blame for the sins of that person. They take part in the sins of other people.
Paul tells Timothy to take care when he lays hands on people. Without due care he may be sharing in their sin, and he must keep himself from sins, both his own and others. Pray earnestly for church leaders, they have a grave responsibility.