KJV: 33 And after they had tarried there a space, they were let go in peace from the brethren unto the apostles. 34 Notwithstanding it pleased Silas to abide there still.
NIV: 33 After spending some time there, they were sent off by the believers with the blessing of peace to return to those who had sent them. 
ESV: 33 And after they had spent some time, they were sent off in peace by the brothers to those who had sent them.
CSB: 33 After spending some time there, they were sent back in peace by the brothers and sisters to those who had sent them.
The problem this addition is trying to solve is caused by v 40, which says that Paul chose Silas. However, v 35 says that Paul and Barnabas stayed in Antioch, and v 32 says that Judas and Silas left Antioch.
A scribe added a clarification that in fact only Judas left, which means Silas was still available for Paul to choose, and it became versified as v 34. Codex C says that Silas remained in Antioch. Codex D says that Silas stayed in Antioch but only Judas had left.
It was a poor solution since v 32 clearly says both Judas and Silas left. There is no reason to think that Silas could not have been elsewhere when Paul selected him, or that time had passed between v 32 and v 40 and Silas had returned to Antioch.
Even the MT omits Acts 15:34.