Jamieson, Fausset and Brown on Numbers 31:6

6. Moses sent ... Eleazar the priest, to the war--Although it is not expressly mentioned, it is highly probable that Joshua was the general who conducted this war. The presence of the priest, who was always with the army (De 20:2), was necessary to preside over the Levites, who accompanied the expedition, and to inflame the courage of the combatants by his sacred services and counsels.

holy instruments--As neither the ark nor the Urim and Thummim were carried to the battlefield till a later period in the history of Israel, the "holy instruments" must mean the "trumpets" (Nu 10:9). And this view is agreeable to the text, by simply changing "and" into "even," as the Hebrew particle is frequently rendered.