Final answer:
RNA Polymerase is the enzyme that can initiate synthesis without a pre-existing primer, unlike DNA polymerase III which requires an RNA primer to begin DNA synthesis.
Step-by-step explanation:
The enzyme that does not require a primer to begin synthesis is RNA Polymerase. DNA polymerase III requires a primer such as an RNA sequence synthesized by primase to provide a free 3'-OH group to which it can add DNA nucleotides. However, RNA polymerases are capable of starting a new nucleic acid strand from scratch without a pre-existing primer, making the synthesis of RNA possible directly against a DNA template.