Between Acts 15:22 and 16:10 some individuals are introduced.
In Acts 15:22 Silas is one of the delegates chosen to accompany Paul and Barnabas back to Antioch with the results of the Jerusalem Council. In verse 40 Paul chooses Silas to go with him to the places that Paul and Barnabas went to earlier.
In 16:1 Paul meets Timothy in Lystra. In verse 3 Paul wants Timothy to go with his growing group and has Timothy circumcised since Timothy has a gentile father and Jewish mother. This can seem to be a strange decision given the whole discussion about circumcision earlier, but Paul looks at each situation, and makes what he believes is the best choice.
Then in verses 6 through 8 the Spirit keeps them from going to certain places, and then in Troas in verse 9 Paul has a vision of a man from Macedonia urging them to come there and help. In verse 10 begins the “we” passages which has led many to conclude that Luke now joins Paul’s group and I have read one biblical scholar speculate that Luke may be the Macedonian urging Paul to come there.