Do I need to get a new J-1 visa in my passport; it expired?

No. The J-1 visa that is in the passport (entrance visa) is needed only to enter the US. The DS- 2019 an individual carries is the legal document that allows them to stay in the U.S. If the exchange visitor plans on travelling internationally for conferences, then they will need to obtain a new visa stamp before re-entering the United States. This can be renewed in the exchange visitor’s home country.