Albert Barnes Commentary Numbers 24:19

"And out of Jacob shall one have dominion, And shall destroy the remnant from the city." — Numbers 24:19 (ASV)

Destroy him that remains of the city — that is, shall destroy those of every city that had previously escaped. The phrase tersely describes a conqueror who first defeats his enemies in battle, and then hunts out the fugitives until he has cut off all from every place (Compare to 1 Kings 11:16).

The victories of David were a partial fulfillment of the predictions (Numbers 24:14, Numbers 24:18), but did not exhaust them.

It is apparent that Edom and Moab are named by Balaam, as they are also by the prophets (for example, Isaiah 11:14), as representatives of the pagan nations (Numbers 24:8) who were hostile to the theocracy. Therefore, just as Jacob figures as a constant type of the Messiah's kingdom in the prophets, so do Edom and Moab represent the enemies of that kingdom. And in the threatened ruin of Edom and Moab is indicated the eventual destruction of all that resist the kingdom of God in its power.

The “Star” and “Sceptre” of the prophecy, like the “Sceptre” and “Lawgiver” of Genesis 49:10, also naturally point to a line of princes rather than to an individual; or rather, they are emblems of the kingdom of Israel generally. Thus, the victories of David and his successors, generation after generation, over Edom and Moab, are unquestionably recurring and progressive fulfillments of what Balaam foretold; but in addition, the prophecy reaches forward to some further and culminating fulfillment, and this also in “the latter days” (Numbers 24:14), the ordinary prophetic designation for the time of the Messiah (compare the marginal references).

To a Christian, the connection between the “Star” and “Sceptre” of Balaam and the “Star of the king of the Jews,” which the wise men saw (Matthew 2:2), is self-evident.