Which organelle that plays a central role in the transport of new molecules from inside to outside the cell?

The Golgi apparatus plays a central role in molecular transport after biosynthesis.

Explanation:

Transcription occurs in the nucleus during protein synthesis, followed by translation inside ribosomes. Then, new molecules join the endoplasmic reticulum to be folded and modified. In the Golgi, they are tagged and separated into lysosomes for export outside the cell.

 The Golgi system comprises of several regions known as cisternae; they act as independent microenvironments where products requiring their own unique conditions are converted into new, stable biomolecules.