In this particular verse, the verb יָרַשׁ (yarash) means “to take possession of, to occupy, especially by force.”1 The occupation of a land typically involved the extermination of the people and property dwelling therein. A prime example of this is Deuteronomy 2:12 which describes how the children of Esau “drove out” the Horims “and destroyed them from their presence and dwelt in their place.”2 In short, in this verse it means to conquer by eliminating any and all presence of the people dwelling in a land.3 It does not mean to let those inhabitants flee in peace and settle elsewhere.
Arie Versluis writes,4
In the Old Testament, a direct command of YHWH to Israel to expel or to destroy the nations of Canaan occurs (outside of Deuteronomy) only in Exod. 23:31 and Num. 33:52.
The verb ירש hif. is not used to describe the requested treatment of the nations in Exod. 23 and Deut. 7. Above, it has been shown that this verb has the sense of “to wipe away, destroy...”
1 p. 370, יָרַשׁ. Gesenius says that the sense of the binyan Hiphil (Hifʿil), (2) that occurs in Num. 33:52 (he specifically cites this verse, among others) is equivalent to the sense of the binyan Kal (Paʿal), (1), (b) (quoted above in my answer).
2 יִירָשׁוּם וַיַּשְׁמִידוּם מִפְּנֵיהֶם וַיֵּשְׁבוּ תַּחְתָּם
3 יָרַשׁ has other usages. For more info, see Gesenius loc. cit.
4 p. 225
Gesenius, Heinrich Friedrich Wilhelm. Gesenius’s Hebrew and Chaldee Lexicon to the Old Testament Scriptures. Trans. Tregelles, Samuel Prideaux. London: Bagster, 1860.
Versluis, Arie. The Command to Exterminate the Canaanites: Deuteronomy 7. Leiden: Brill, 2017.