In terms of chronology, the movie for the most part occurs in parallel with the original 300 movie.
However, there are events which occur both before and after the original 300 movie.
Events which occur before include: Battle of Marathon and Xerxes becoming the God-King.
Events occurring after include Themistocles visit to Gorgo (where she is still mourning King Leonidas) and the Battle of Salamis.
*300: Rise of an Empire is a prequel, a side-sequel, and a sequel to the original film, 300 (2007), with the events in the follow-up taking place before, during, and after the events in the original. The first battle that takes place in the 300: Rise of an Empire movie is the Battle of Marathon in 490 BC. This happens ten years prior to the events in 2007's 300 movie. Athens victory over Persia at Marathon, Greece sets the stage for the motivations behind Xerxes's transformation into the movie's fictional God King.
The second battle that occurs in 300: Rise of an Empire, the Battle of Artemisium (a 480 BC naval engagement), took place concurrently with the Battle of Thermopylae that unfolds in the original movie, 300. It was Themistocles who proposed that the Greeks attempt to stop the Persian advance by confronting them on land at the narrow strait at Thermopylae. Leonidas and the 300 Spartans undertook the task, which is chronicled in the movie 300, with the Spartans eventually being overtaken by the Persian forces. At the same time, the Greek navy attempted to block the Persians on the water in the Straits of Artemisium. However, they were forced to retreat after the defeat at Thermopylae.
The third battle in Rise of an Empire, the Battle of Salamis, occurs after the Persians have advanced and burned Athens to the ground. Like in the movie, Themistocles had learned from the mistakes he made in the Battle of Artemisium, realizing that Greece likely did not stand a chance when confronting the larger Persian navy in the open water. He figured out that if the Greeks were to win, they would need to engage in close combat with the Persians in straits that were narrower, such as those at Salamis. There, the large Persian warships could be outmaneuvered by the smaller Greek ships.