The “prince” is first mentioned in Ezekiel 34:24 where it appears to refer to David, although David had been dead for 400 years when Ezekiel wrote this.
The Messiah will be the King sitting upon the throne of David. Ezekiel 44:3 says only the prince can use the East Gate. The residue shall be for the prince on the one side and on the other, &c. — The prince’s part shall be extended, both on the east and west side of the several allotments belonging to the priests, the Levites, and the city. Jack Kelley, Ask A Bible Teacher Wednesday, January 7th, 2015 Q. Ezekiel 48:21 mentions the property belonging to the “prince”, who is the prince? Thus, reference to what is possible within the history of this age becomes shadowy again. Then in Ezekiel 37:24 God had Ezekiel say that David will be their king, but in Ezekiel 37:25 He said David will be their prince forever. According to Ezekiel 44:2,3, it is this prince who only approaches the throne. A. Ezekiel 45:7 tells us the prince will be given land surrounding the property of the Holy City and the Temple. The princely line that cheated on the offerings is finished: the prince cannot within Ezekiel’s purview be a reformed successor to Zedekiah.

Who Is The Prince? Over against the five and twenty thousand, &c. Ezekiel 48:21. Since the prince of Ezekiel 45:17 does not sit on a throne, he cannot be the Messiah.