C. F. Keil and Franz Delitzsch on Deuteronomy 21:5

Deu 21:5

The priests were to come near during this transaction; i.e., some priests from the nearest Levitical town were to be present at it, not to conduct the affair, but as those whom Jehovah had chosen to serve Him and to bless in His name (cf. Deu 13:5), and according to whose mouth (words) every dispute and every stroke happened (cf. Deu 17:8), i.e., simply as those who were authorized by the Lord, and as the representatives of the divine right, to receive the explanation and petition of the elders, and acknowledge the legal validity of the act.