Note that the following verse also uses the singular noun. Note the use of the definitive article:
"But the prophet, that shall speak a word presumptuously in My name, which I have not commanded him to speak, or that shall speak in the name of other gods, that same prophet shall die.'"
See also Deut. 13:2 which also deals with a false prophet:
"If there arise in the midst of thee a prophet..."
The language is the same. Here the same term for "arise/raise" is used.
Clearly, there were many false prophets, so obviously the verse is not talking about a singular definitive false prophet. It stands to reason that the early verses are also not exclusive to a single prophet. Indeed, these verses are the source for the commandment to listen to the words of a true prophet. Obviously, this commandment refers to all true prophets through history. For details of this commandment see Maimonide's Sefer HaMitzvot, Positive Command #172. The Chabad website provides a full English translation.
The significance of the phrase "God raise up" can be seen by reading Maimonides' explanation of prophecy in his Guide For The Perplexed, part II, chapter 32. He states that there are three opinions of how one achieves prophecy. The first opinion is that God chooses anyone He desires to be a prophet, even if that individual is a fool and not particularly pious. The second opinion is that anyone who studies and perfects his faculties will necessarily prophesize. Maimonides rejects both these opinions and maintains that only an individual who has prepared himself for prophecy and whom God chooses to inspire will prophesize. (That's it in a rather crude nutshell- please consult the Guide for the full treatment.) So the verse is telling us that not every wise and righteous individual will necessarily prophesize, it's only one who "God raises up" who shall deliver prophecy.