The interpretation of the last chapters of Ezekiel is strongly debated. Obviously, how a person views what these chapters envision will impact the interpretation of the various elements, such as the prince.
First, we must note that this vision does not deal with the physical world. For example, the size of the territory described would not fit in Israel’s boundaries with Jerusalem being at the center. The layout of the country is in rectangles, not following the natural boundaries of a physical land. It even speaks of a river (Ezekiel 47:1-2) that doesn’t exist and which rapidly becomes deep without any tributaries. It is not a natural river. Given this, the vision is illustrating concepts and not people, places, or things.
Next, we note that a prince is not a king. He is a ruler to acts on behalf of the king. Take notice of Ezekiel 45:8 especially. It talks of multiple princes seeming to indicate that there will be a series of rulers. Ezekiel 46:16 also refers to the prince’s sons. The prince’s land was two large tracts on either side of the sanctuary’s land. The reason given is “so My princes shall no longer oppress My people” (Ezekiel 45:8). Earlier in Ezekiel, this was a charge against the princes of Israel. “Her princes within her are like wolves tearing the prey, by shedding blood and destroying lives in order to get dishonest gain” (Ezekiel 22:27). God then commands the princes to no longer oppress His people (Ezekiel 45:9). This is further supported by Ezekiel 46:18, “The prince shall not take from the people’s inheritance, thrusting them out of their inheritance.” This appears to be a reference to Ahab who took Naboth’s vineyard.
The prince is to offer sacrifices on behalf of God’s people (Ezekiel 45:22-25). The east gate is kept closed except on the days when the prince enters to bring his sacrifices (Ezekiel 46:1-2,12).
Some see the prince as being Jesus, but the description doesn’t match Jesus in many ways. For instance, Jesus would not need commands not to oppress God’s people. Jesus offered himself once as a sacrifice, but this vision involves continual sacrifices.
Most likely this is a spiritual vision of the church. In which case, the princes would be the elders (Hebrews 13:17). They are to abide near the center of the worship of God. They are warned not to exploit God’s people (I Peter 5:1-4). They are to offer up prayers for the sick (James 5:14-15).