According to the Mosaic Law in the book of Numbers it seems the Levites were the ones who were ordained to collect the Tithes.
Numbers 18:21 NIV
21 “I give to the Levites all the tithes in Israel as their inheritance in return for the work they do while serving at the tent of meeting.
Numbers 18:24 NIV
24 Instead, I give to the Levites as their inheritance the tithes that the Israelites present as an offering to the Lord. That is why I said concerning them: ‘They will have no inheritance among the Israelites.’”
But the letter to the Hebrews it seems to allude to the Priesthood as ones ordained to collect tithes from the people
Hebrews 7:5 NIV
Now the law requires the descendants of Levi who become priests to collect a tenth from the people—that is, from their fellow Israelites—even though they also are descended from Abraham.
Who collected Tithes from the people?